SlideShare una empresa de Scribd logo
1 de 8
Descargar para leer sin conexión
Subtract 1
2 mark for reducible fractions or incorrect rounding.
Question marks: 4, 7, 6, 15, 5, 11, 16, 9, 9,18
1. (a) Simplify 6x3
+ 8y − 7x3
− 14y + 2x3
(2 marks)
x3
− 6y
1 mark per term
(b) Evaluate y3
x when y = 2 and x = 4. (2 marks)
23
4 = 8
4 = 2
2 marks soln, 1 mark working but incorrect soln
2. (a) What is the equation of the line passing through the point (4, 3) with gradient
1
2 ? (3 marks)
3 = 1
2 × 4 + c (1 mark)
c = 1 (1 mark)
y = 1
2 x + 1 (1 mark)
(b) Solve the simultaneous equations (4 marks)
x −2y = −2
x −y = −4
y = −2 (2 marks)
x = −6 (2 marks)
3. A farmer keeps track of how many eggs his hens lay.
2 2 4 3 5 4 4 2 4
(a) What is the mode? (1 marks)
Mode is 4.
(b) What is the median? (2 marks)
Ordered data: 2 2 2 3 4 4 4 4 5
9 × 1
2 = 4.5
Median=4
1 mark ordered table 1 mark median
(c) What is the interquartile range? (3 marks)
9 × 1
4 = 2.25
Q1 = 2 (1 mark)
9 × 3
4 = 6.75
Q3 = 4 (1 mark)
IQR= 4 − 2 = 2 (1 mark)
4. Sloths should have a mean of 16.5 hours sleep a day. A sloth owner wants to see if his sloths are
sleeping too much and collects the following data.
17 18 20 19 16
(a) State the null hypothesis and the alternative hypothesis. (2 marks)
H0 : µ = 16.5
H1 : µ > 16.5
1 mark for 16.5, 1 mark for >, -1 mark if no µ
1
(b) What is the mean of the test data? (2 marks)
µ(X) = 90
5 = 18
2 marks for correct soln, 1 mark if correct working incorrect sol
(c) What is the sample standard deviation of the test data? (4 marks)
σ2
(X) = 1630−5×182
4 = 2.5
σ(X) = 1.5811
1 mark sum of squares, 1 mark working, 1 mark sample var, 1 mark soln
(d) What is the T test statistic? (3 marks)
T = 18−16.5
1.5811/
√
5
= 2.121
1 mark identifying vars, 1 mark working, 1 mark soln
(e) The study is taken with a 1% level of significance. What is the critical T value? (2
marks)
df = 5 − 1 = 4 (1 mark)
1%, 1 tail, df = 4
C = 3.747 (1 mark)
(f) What can we deduce? (2 marks)
2.121 < 3.747 (1 mark)
Accept H0 (1 mark)
5. Consider the following triangle.
34
60
h
(a) What is the length h to 2 d.p.? (2 mark)
sin(60) = h
3 (1 mark)
h = 2.60 (1 mark)
(b) What is the area of the triangle 1 d.p.? (3 marks)
Right triangle:
Area = 1
2 × 2.60 × 3 × sin(30) = 1.95 (1 mark)
Left triangle:√
42 − 2.602 = 3.04
Area = 1
2 × 3.04 × .2.60 = 3.95 (1 mark)
Area= 3.04 + 3.95 = 7. (1 mark)
6. Solve the following quadratic equations using the method stated. No points will be awarded
if another method is used. Leave answers in surd form.
(a) 3x2
+ 12x + 5 = 0. Solve by using the quadratic formula. (4 marks)
a = 3, b = 12, c = 5
x = −12±
√
122−4×3×5
2×3 = −6±
√
21
3
1 mark identifying a,b,c, 1 mark working, 2 marks soln
(b) x2
− x − 6 = 0. Solve by factorising. (2 marks)
(x − 3)(x + 2) = 0 (1 mark)
2
x = −2, 3 (1 mark)
(c) x2
+ 10x + 6 = 0. Solve by completing the square. (5 marks)
(x + 5)2
− 25 + 6 = 0 (2 marks)
(x + 5)2
= 19 (1 mark)
x + 5 =
√
19 (1 mark)
x = −5 ±
√
19 (1 mark)
7. A researcher wants to show that height and baldness are independent. He collects the following
data;
Short Average Tall
Luxuriant 6 6 8
Thinning 7 8 5
Bald 2 16 2
(a) State the null hypothesis and the alternative hypothesis. (2 marks)
H0 : There is no correlation. (1 mark)
H1 : there is a correlation. (1 mark)
1 mark if reversed
(b) What is the χ2
test statistic? (10 marks)
Totals:
Short Average Tall Row total
Luxuriant 6 6 8 20
Thinning 7 8 5 20
Bald 2 16 2 20
Column total 15 30 15 60
Fit:
5 10 5
5 10 5
5 10 5
Residual:
1 -4 3
2 -2 0
-3 6 -3
χ2
table:
0.2 1.6 1.8
0.8 0.4 0
1.8 3.6 1.8
χ2
= 12
2 marks per table, −1
2 per error, −1
2 per table with rounding errors, 2 marks for soln
(c) If we test at a 5% level of significance what is the critical χ2
value? (2 marks)
df = (3 − 1)(3 − 1) = 4 (1 mark)
C = 9.49 (1 mark)
(d) What can we deduce? (2 marks)
9.49 < 12 (1 mark)
Reject H0. (1 mark)
3
8. (a) Show that there is a solution to x6
− 5x + 2 = 0 for some x between 0 and 1. (3 marks)
Set f(x) = x6
− 5x + 2
f(0) = 2 (1 mark)
f(1) = −2 (1 mark)
f(0) > 0, f(1) < 0 so there is a soln to f(x) = 0 for some x between 0 and 1. (1 mark)
(b) Use trial and improvement to find a solution to 1 d.p. (6 marks)
x f(x) Soln between
0.5 -0.48 0 and 0.5
0.3 0.5 0.3 and 0.5
0.4 0.004 0.4 and 0.5
0.45 -0.24 0.4 and 0.45
Soln is 0.4 to 1 d.p.
3 marks working, 1 mark midpoint, 2 marks soln
9. An airship has speed v = 4t − 100t−2
.
(a) What is the speed of the airship when t = 10? (1 mark)
v(10) = 4 × 10 − 100 × 10−2
= 39
(b) What is the airships acceleration as a function of time? (3 marks)
a = dv
dt = 4 + 200t−3
1 mark differentiating, 1 mark per term
(c) When t = 10 the distance x = 262. Write the distance the rocket travels as a
function of time. (5 marks)
x = vdt
= 4t − 100t−2
dt
= 2t2
+ 100t−1
+ C
262 = 2 × 102
+ 100 × 10−1
+ C
C = 52
x = 2t2
+ 100t−1
+ 52
2 marks for integrating, 1 mark for substituting, 1 mark for c, 1 mark for soln
10. (a) Differentiate y = 8x3
− 2x. (2 marks)
dy
dx = 24x2
− 2
1 mark per term
(b) What are the x and y co-ordinates of the stationary points of the graph
y = 8x3
− 2x? (4 marks)
dy
dx = 0
24x2
− 2 = 0
x2
= 1
12
x = ± 1√
12
= ±0.29 (2 marks)
y( 1√
12
) = − 4
3
√
12
= −0.38 (1 mark)
y(− 1√
12
) = 4
3
√
12
= 0.38 (1 mark)
(c) What are the natures of these stationary points? (3 marks)
d2
y
dx2 = 48x (1 mark)
d2
y
dx2 ( 1√
12
) = 4
√
12 > 0 Minimum (1 mark)
d2
y
dx2 (− 1√
12
) = −4
√
12 < 0 Maximum (1 mark)
4
(d) Sketch the graph y = 8x3
− 2x making sure to label your sketch clearly. (5 marks)
−0.5 −0.29 0.29 0.5
−0.38
0.38
x
y
1 mark per stat point, 2 marks for intercepts, 1 mark for shape
(e) By integrating, find the area under the graph y = 8x3
− 2x between the
values x = −0.5 and x = 0.5. (4 marks)
0.5
−0.5
8x3
− 2xdx = [2x4
− x2
]0.5
−0.5
= (2 × 0.54
− 0.52
) − (2 × (−0.5)4
− (−0.5)2
)
= 0
2 marks integral, 1 mark subs, 1 mark soln
5
Formulae
Let X be a list of data of size n.
Mean:
µ(X) =
n
i=1 X[i]
n
Variance
σ2
(X) =
n
i=1(X[i])2
n
− µ2
(X)
Z-statistic
Z =
µ(X) − µ
σ/
√
n
Sample Variance
σ2
(X) =
n
i=1(X[i])2
− nµ2
(X)
n − 1
T-statistic
T =
µ(X) − µ
σ(X)/
√
n
Alternative notation
Mean
¯x =
x
n
Variance
V ar =
x2
n
− ¯x2
Z-statistic
Z =
¯x − A
σ/
√
n
Sample Variance
s2
=
x2
− n¯x2
n − 1
T-statistic
T =
¯x − A
s/
√
n
6
Pythagoras’ Theorem
a2
+ b2
= c2
tan(A) =
opp
adj
, cos(A) =
adj
hyp
, sin(A) =
opp
hyp
Sine rule
a
sin(A)
=
b
sin(B)
=
c
sin(C)
Cosine rule
a2
= b2
+ c2
− 2bc cos(A)
Area
Area = 1/2ab sin(C)
Quadratic formula
x =
−b ±
√
b2 − 4ac
2a
Equation of a straight line
y = mx + c
Gradient of a straight line
m =
y2 − y1
x2 − x1
χ2
Process
1. We refer to the entry in the ith
column and the jth
row as M(i, j).
2. Calculate the row totals Ri, the column totals Ci and the overall total T.
3. Construct the fit table. The entry in the ith
column and jth
row is given by:
F(i, j) =
Ci × Rj
T
4. Construct the residual table. The entry in the ith
column and jth
row is given by:
R(i, j) = M(i, j) − F(i, j)
5. Construct the χ2
-table. The entry in the ith
column and jth
row is given by:
χ2
(i, j) =
R(i, j)2
F(i, j)
7
Tables
Critical Z-values
Sig. Lev. 5% Sig. Lev. 1%
One-tail Two-tail One-tail Two-tail
Probability 0.05 0.025 0.01 0.005
Critical value 1.65 1.96 2.33 2.58
Critical T-values
Sig. Lev. 5% Sig. Lev. 1%
One-tail Two-tail One-tail Two-tail
d.f. 0.05 0.025 0.01 0.005
1 6.314 12.706 31.821 63.656
2 2.920 4.303 6.965 9.925
3 2.353 3.182 4.541 5.841
4 2.132 2.776 3.747 4.604
5 2.015 2.571 3.365 4.032
6 1.943 2.447 3.143 3.707
7 1.895 2.365 2.998 3.499
8 1.860 2.306 2.896 3.355
9 1.833 2.262 2.821 3.250
10 1.812 2.228 2.764 3.169
Critical χ2
value
5% significance 1% Significance
df Probability 0.05 Probability 0.01
1 3.84 6.63
2 5.99 9.21
3 7.81 11.3
4 9.49 13.3
5 11.1 15.1
6 12.6 16.8
7 14.1 18.5
8 15.5 20.1
9 16.9 21.7
10 18.3 23.2
11 19.7 24.7
12 21.0 26.2
8

Más contenido relacionado

La actualidad más candente

Quadratic Equations (Quadratic Formula) Using PowerPoint
Quadratic Equations (Quadratic Formula) Using PowerPointQuadratic Equations (Quadratic Formula) Using PowerPoint
Quadratic Equations (Quadratic Formula) Using PowerPointrichrollo
 
Modul bimbingan add maths
Modul bimbingan add mathsModul bimbingan add maths
Modul bimbingan add mathsSasi Villa
 
Quadratic And Roots
Quadratic And RootsQuadratic And Roots
Quadratic And RootsPeking
 
Chapter 5 indices & logarithms
Chapter 5  indices & logarithmsChapter 5  indices & logarithms
Chapter 5 indices & logarithmsatiqah ayie
 
16.2 Solving by Factoring
16.2 Solving by Factoring16.2 Solving by Factoring
16.2 Solving by Factoringswartzje
 
Algebra Project Period 4
Algebra Project Period 4Algebra Project Period 4
Algebra Project Period 4ingroy
 
Add maths module form 4 & 5
Add maths module form 4 & 5Add maths module form 4 & 5
Add maths module form 4 & 5smktsj2
 
Cbse 12 Class Maths Sample Papers Model 4
Cbse 12 Class Maths Sample Papers Model 4 Cbse 12 Class Maths Sample Papers Model 4
Cbse 12 Class Maths Sample Papers Model 4 Sunaina Rawat
 
Chapter 3 quadratc functions
Chapter 3  quadratc functionsChapter 3  quadratc functions
Chapter 3 quadratc functionsatiqah ayie
 
Chapter 4 simultaneous equations
Chapter 4  simultaneous equationsChapter 4  simultaneous equations
Chapter 4 simultaneous equationsatiqah ayie
 
Spm add math 2009 paper 1extra222
Spm add math 2009 paper 1extra222Spm add math 2009 paper 1extra222
Spm add math 2009 paper 1extra222Saripah Ahmad Mozac
 
Higher Maths 2.1.2 - Quadratic Functions
Higher Maths 2.1.2 - Quadratic FunctionsHigher Maths 2.1.2 - Quadratic Functions
Higher Maths 2.1.2 - Quadratic Functionstimschmitz
 
Strategic Intervention Materials
Strategic Intervention MaterialsStrategic Intervention Materials
Strategic Intervention MaterialsBrian Mary
 

La actualidad más candente (19)

Nota math-spm
Nota math-spmNota math-spm
Nota math-spm
 
Quadratic Equations (Quadratic Formula) Using PowerPoint
Quadratic Equations (Quadratic Formula) Using PowerPointQuadratic Equations (Quadratic Formula) Using PowerPoint
Quadratic Equations (Quadratic Formula) Using PowerPoint
 
Modul bimbingan add maths
Modul bimbingan add mathsModul bimbingan add maths
Modul bimbingan add maths
 
Ceramah Add Mth
Ceramah Add MthCeramah Add Mth
Ceramah Add Mth
 
Quadratic And Roots
Quadratic And RootsQuadratic And Roots
Quadratic And Roots
 
Chapter 5 indices & logarithms
Chapter 5  indices & logarithmsChapter 5  indices & logarithms
Chapter 5 indices & logarithms
 
Irasional
IrasionalIrasional
Irasional
 
16.2 Solving by Factoring
16.2 Solving by Factoring16.2 Solving by Factoring
16.2 Solving by Factoring
 
Algebra Project Period 4
Algebra Project Period 4Algebra Project Period 4
Algebra Project Period 4
 
Add maths module form 4 & 5
Add maths module form 4 & 5Add maths module form 4 & 5
Add maths module form 4 & 5
 
Cbse 12 Class Maths Sample Papers Model 4
Cbse 12 Class Maths Sample Papers Model 4 Cbse 12 Class Maths Sample Papers Model 4
Cbse 12 Class Maths Sample Papers Model 4
 
Chapter 3 quadratc functions
Chapter 3  quadratc functionsChapter 3  quadratc functions
Chapter 3 quadratc functions
 
Class XII CBSE Mathematics Sample question paper with solution
Class XII CBSE Mathematics Sample question paper with solutionClass XII CBSE Mathematics Sample question paper with solution
Class XII CBSE Mathematics Sample question paper with solution
 
Chapter 4 simultaneous equations
Chapter 4  simultaneous equationsChapter 4  simultaneous equations
Chapter 4 simultaneous equations
 
Spm add math 2009 paper 1extra222
Spm add math 2009 paper 1extra222Spm add math 2009 paper 1extra222
Spm add math 2009 paper 1extra222
 
Higher Maths 2.1.2 - Quadratic Functions
Higher Maths 2.1.2 - Quadratic FunctionsHigher Maths 2.1.2 - Quadratic Functions
Higher Maths 2.1.2 - Quadratic Functions
 
Form 4 add maths note
Form 4 add maths noteForm 4 add maths note
Form 4 add maths note
 
Strategic Intervention Materials
Strategic Intervention MaterialsStrategic Intervention Materials
Strategic Intervention Materials
 
Final exam review #2
Final exam review #2Final exam review #2
Final exam review #2
 

Destacado

Lecture 10 handout
Lecture 10 handoutLecture 10 handout
Lecture 10 handoutfatima d
 
Lecture 13 contract law
Lecture 13 contract lawLecture 13 contract law
Lecture 13 contract lawfatima d
 
C2 st lecture 10 basic statistics and the z test handout
C2 st lecture 10   basic statistics and the z test handoutC2 st lecture 10   basic statistics and the z test handout
C2 st lecture 10 basic statistics and the z test handoutfatima d
 
Lecture 11 law of tort
Lecture 11  law of tort Lecture 11  law of tort
Lecture 11 law of tort fatima d
 
Questions to Answer Before Filing Bankruptcy
Questions to Answer Before Filing BankruptcyQuestions to Answer Before Filing Bankruptcy
Questions to Answer Before Filing BankruptcyDavid M. Offen
 

Destacado (6)

Lecture 10 handout
Lecture 10 handoutLecture 10 handout
Lecture 10 handout
 
Expert Advice and Goals for 2015
Expert Advice and Goals for 2015Expert Advice and Goals for 2015
Expert Advice and Goals for 2015
 
Lecture 13 contract law
Lecture 13 contract lawLecture 13 contract law
Lecture 13 contract law
 
C2 st lecture 10 basic statistics and the z test handout
C2 st lecture 10   basic statistics and the z test handoutC2 st lecture 10   basic statistics and the z test handout
C2 st lecture 10 basic statistics and the z test handout
 
Lecture 11 law of tort
Lecture 11  law of tort Lecture 11  law of tort
Lecture 11 law of tort
 
Questions to Answer Before Filing Bankruptcy
Questions to Answer Before Filing BankruptcyQuestions to Answer Before Filing Bankruptcy
Questions to Answer Before Filing Bankruptcy
 

Similar a Foundation c2 exam june 2013 resit 2 sols

Foundation c2 exam may 2013 sols
Foundation c2 exam may 2013 solsFoundation c2 exam may 2013 sols
Foundation c2 exam may 2013 solsfatima d
 
Foundation c2 exam august 2012 sols
Foundation c2 exam august 2012 solsFoundation c2 exam august 2012 sols
Foundation c2 exam august 2012 solsfatima d
 
Banco de preguntas para el ap
Banco de preguntas para el apBanco de preguntas para el ap
Banco de preguntas para el apMARCELOCHAVEZ23
 
Bt0063 mathematics fot it
Bt0063 mathematics fot itBt0063 mathematics fot it
Bt0063 mathematics fot itnimbalkarks
 
Straight-Line-Graphs-Final -2.pptx
Straight-Line-Graphs-Final -2.pptxStraight-Line-Graphs-Final -2.pptx
Straight-Line-Graphs-Final -2.pptxKviskvis
 
algebraic_concepts_1.pdf
algebraic_concepts_1.pdfalgebraic_concepts_1.pdf
algebraic_concepts_1.pdfShaniekaMaxwell
 
ISI MSQE Entrance Question Paper (2008)
ISI MSQE Entrance Question Paper (2008)ISI MSQE Entrance Question Paper (2008)
ISI MSQE Entrance Question Paper (2008)CrackDSE
 
23NCBSE09MAT02TP103V01L1_Polynomials_Factorisation_of_Polynomials.pdf
23NCBSE09MAT02TP103V01L1_Polynomials_Factorisation_of_Polynomials.pdf23NCBSE09MAT02TP103V01L1_Polynomials_Factorisation_of_Polynomials.pdf
23NCBSE09MAT02TP103V01L1_Polynomials_Factorisation_of_Polynomials.pdffatimashifali
 
Zhejiang University of TechnologyMATH 011 Calculus IFin.docx
Zhejiang University of TechnologyMATH 011 Calculus IFin.docxZhejiang University of TechnologyMATH 011 Calculus IFin.docx
Zhejiang University of TechnologyMATH 011 Calculus IFin.docxlynnalix61619
 
IIT Jam math 2016 solutions BY Trajectoryeducation
IIT Jam math 2016 solutions BY TrajectoryeducationIIT Jam math 2016 solutions BY Trajectoryeducation
IIT Jam math 2016 solutions BY TrajectoryeducationDev Singh
 
2014 st josephs geelong spec maths
2014 st josephs geelong spec maths2014 st josephs geelong spec maths
2014 st josephs geelong spec mathsAndrew Smith
 
Aieee 2003 maths solved paper by fiitjee
Aieee 2003 maths solved paper by fiitjeeAieee 2003 maths solved paper by fiitjee
Aieee 2003 maths solved paper by fiitjeeMr_KevinShah
 

Similar a Foundation c2 exam june 2013 resit 2 sols (14)

Foundation c2 exam may 2013 sols
Foundation c2 exam may 2013 solsFoundation c2 exam may 2013 sols
Foundation c2 exam may 2013 sols
 
Foundation c2 exam august 2012 sols
Foundation c2 exam august 2012 solsFoundation c2 exam august 2012 sols
Foundation c2 exam august 2012 sols
 
Banco de preguntas para el ap
Banco de preguntas para el apBanco de preguntas para el ap
Banco de preguntas para el ap
 
Bt0063 mathematics fot it
Bt0063 mathematics fot itBt0063 mathematics fot it
Bt0063 mathematics fot it
 
add math form 4/5
add math form 4/5add math form 4/5
add math form 4/5
 
Straight-Line-Graphs-Final -2.pptx
Straight-Line-Graphs-Final -2.pptxStraight-Line-Graphs-Final -2.pptx
Straight-Line-Graphs-Final -2.pptx
 
algebraic_concepts_1.pdf
algebraic_concepts_1.pdfalgebraic_concepts_1.pdf
algebraic_concepts_1.pdf
 
EPCA_MODULE-2.pptx
EPCA_MODULE-2.pptxEPCA_MODULE-2.pptx
EPCA_MODULE-2.pptx
 
ISI MSQE Entrance Question Paper (2008)
ISI MSQE Entrance Question Paper (2008)ISI MSQE Entrance Question Paper (2008)
ISI MSQE Entrance Question Paper (2008)
 
23NCBSE09MAT02TP103V01L1_Polynomials_Factorisation_of_Polynomials.pdf
23NCBSE09MAT02TP103V01L1_Polynomials_Factorisation_of_Polynomials.pdf23NCBSE09MAT02TP103V01L1_Polynomials_Factorisation_of_Polynomials.pdf
23NCBSE09MAT02TP103V01L1_Polynomials_Factorisation_of_Polynomials.pdf
 
Zhejiang University of TechnologyMATH 011 Calculus IFin.docx
Zhejiang University of TechnologyMATH 011 Calculus IFin.docxZhejiang University of TechnologyMATH 011 Calculus IFin.docx
Zhejiang University of TechnologyMATH 011 Calculus IFin.docx
 
IIT Jam math 2016 solutions BY Trajectoryeducation
IIT Jam math 2016 solutions BY TrajectoryeducationIIT Jam math 2016 solutions BY Trajectoryeducation
IIT Jam math 2016 solutions BY Trajectoryeducation
 
2014 st josephs geelong spec maths
2014 st josephs geelong spec maths2014 st josephs geelong spec maths
2014 st josephs geelong spec maths
 
Aieee 2003 maths solved paper by fiitjee
Aieee 2003 maths solved paper by fiitjeeAieee 2003 maths solved paper by fiitjee
Aieee 2003 maths solved paper by fiitjee
 

Más de fatima d

10 terrorism
10 terrorism10 terrorism
10 terrorismfatima d
 
09 non governmental organisations
09  non governmental organisations09  non governmental organisations
09 non governmental organisationsfatima d
 
17 china and the developing world
17 china and the developing world17 china and the developing world
17 china and the developing worldfatima d
 
16 development assistance
16 development assistance16 development assistance
16 development assistancefatima d
 
15 development issues
15 development issues15 development issues
15 development issuesfatima d
 
12b beyond unipolarity
12b beyond unipolarity12b beyond unipolarity
12b beyond unipolarityfatima d
 
12a beyond bipolarity fukuyama and huntington
12a  beyond bipolarity   fukuyama and huntington12a  beyond bipolarity   fukuyama and huntington
12a beyond bipolarity fukuyama and huntingtonfatima d
 
Un covenant economioc social cultural
Un covenant economioc social culturalUn covenant economioc social cultural
Un covenant economioc social culturalfatima d
 
Un covenant civil political rights
Un covenant civil political rightsUn covenant civil political rights
Un covenant civil political rightsfatima d
 
Cairo declaration 1990
Cairo declaration 1990Cairo declaration 1990
Cairo declaration 1990fatima d
 
Un declaration of human rights
Un declaration of human rightsUn declaration of human rights
Un declaration of human rightsfatima d
 
C2 st lecture 6 handout
C2 st lecture 6 handoutC2 st lecture 6 handout
C2 st lecture 6 handoutfatima d
 
C2 st lecture 5 handout
C2 st lecture 5 handoutC2 st lecture 5 handout
C2 st lecture 5 handoutfatima d
 
C2 st lecture 4 handout
C2 st lecture 4 handoutC2 st lecture 4 handout
C2 st lecture 4 handoutfatima d
 
C2 st lecture 3 handout
C2 st lecture 3 handoutC2 st lecture 3 handout
C2 st lecture 3 handoutfatima d
 
C2 st lecture 2 handout
C2 st lecture 2 handoutC2 st lecture 2 handout
C2 st lecture 2 handoutfatima d
 
C2 st lecture 8 pythagoras and trigonometry handout
C2 st lecture 8   pythagoras and trigonometry handoutC2 st lecture 8   pythagoras and trigonometry handout
C2 st lecture 8 pythagoras and trigonometry handoutfatima d
 
C2 st lecture 9 probability handout
C2 st lecture 9   probability handoutC2 st lecture 9   probability handout
C2 st lecture 9 probability handoutfatima d
 
C2 st lecture 11 the t-test handout
C2 st lecture 11   the t-test handoutC2 st lecture 11   the t-test handout
C2 st lecture 11 the t-test handoutfatima d
 
C2 st lecture 12 the chi squared-test handout
C2 st lecture 12   the chi squared-test handoutC2 st lecture 12   the chi squared-test handout
C2 st lecture 12 the chi squared-test handoutfatima d
 

Más de fatima d (20)

10 terrorism
10 terrorism10 terrorism
10 terrorism
 
09 non governmental organisations
09  non governmental organisations09  non governmental organisations
09 non governmental organisations
 
17 china and the developing world
17 china and the developing world17 china and the developing world
17 china and the developing world
 
16 development assistance
16 development assistance16 development assistance
16 development assistance
 
15 development issues
15 development issues15 development issues
15 development issues
 
12b beyond unipolarity
12b beyond unipolarity12b beyond unipolarity
12b beyond unipolarity
 
12a beyond bipolarity fukuyama and huntington
12a  beyond bipolarity   fukuyama and huntington12a  beyond bipolarity   fukuyama and huntington
12a beyond bipolarity fukuyama and huntington
 
Un covenant economioc social cultural
Un covenant economioc social culturalUn covenant economioc social cultural
Un covenant economioc social cultural
 
Un covenant civil political rights
Un covenant civil political rightsUn covenant civil political rights
Un covenant civil political rights
 
Cairo declaration 1990
Cairo declaration 1990Cairo declaration 1990
Cairo declaration 1990
 
Un declaration of human rights
Un declaration of human rightsUn declaration of human rights
Un declaration of human rights
 
C2 st lecture 6 handout
C2 st lecture 6 handoutC2 st lecture 6 handout
C2 st lecture 6 handout
 
C2 st lecture 5 handout
C2 st lecture 5 handoutC2 st lecture 5 handout
C2 st lecture 5 handout
 
C2 st lecture 4 handout
C2 st lecture 4 handoutC2 st lecture 4 handout
C2 st lecture 4 handout
 
C2 st lecture 3 handout
C2 st lecture 3 handoutC2 st lecture 3 handout
C2 st lecture 3 handout
 
C2 st lecture 2 handout
C2 st lecture 2 handoutC2 st lecture 2 handout
C2 st lecture 2 handout
 
C2 st lecture 8 pythagoras and trigonometry handout
C2 st lecture 8   pythagoras and trigonometry handoutC2 st lecture 8   pythagoras and trigonometry handout
C2 st lecture 8 pythagoras and trigonometry handout
 
C2 st lecture 9 probability handout
C2 st lecture 9   probability handoutC2 st lecture 9   probability handout
C2 st lecture 9 probability handout
 
C2 st lecture 11 the t-test handout
C2 st lecture 11   the t-test handoutC2 st lecture 11   the t-test handout
C2 st lecture 11 the t-test handout
 
C2 st lecture 12 the chi squared-test handout
C2 st lecture 12   the chi squared-test handoutC2 st lecture 12   the chi squared-test handout
C2 st lecture 12 the chi squared-test handout
 

Último

Education and training program in the hospital APR.pptx
Education and training program in the hospital APR.pptxEducation and training program in the hospital APR.pptx
Education and training program in the hospital APR.pptxraviapr7
 
The basics of sentences session 10pptx.pptx
The basics of sentences session 10pptx.pptxThe basics of sentences session 10pptx.pptx
The basics of sentences session 10pptx.pptxheathfieldcps1
 
Drug Information Services- DIC and Sources.
Drug Information Services- DIC and Sources.Drug Information Services- DIC and Sources.
Drug Information Services- DIC and Sources.raviapr7
 
Patterns of Written Texts Across Disciplines.pptx
Patterns of Written Texts Across Disciplines.pptxPatterns of Written Texts Across Disciplines.pptx
Patterns of Written Texts Across Disciplines.pptxMYDA ANGELICA SUAN
 
CapTechU Doctoral Presentation -March 2024 slides.pptx
CapTechU Doctoral Presentation -March 2024 slides.pptxCapTechU Doctoral Presentation -March 2024 slides.pptx
CapTechU Doctoral Presentation -March 2024 slides.pptxCapitolTechU
 
Benefits & Challenges of Inclusive Education
Benefits & Challenges of Inclusive EducationBenefits & Challenges of Inclusive Education
Benefits & Challenges of Inclusive EducationMJDuyan
 
Diploma in Nursing Admission Test Question Solution 2023.pdf
Diploma in Nursing Admission Test Question Solution 2023.pdfDiploma in Nursing Admission Test Question Solution 2023.pdf
Diploma in Nursing Admission Test Question Solution 2023.pdfMohonDas
 
Patient Counselling. Definition of patient counseling; steps involved in pati...
Patient Counselling. Definition of patient counseling; steps involved in pati...Patient Counselling. Definition of patient counseling; steps involved in pati...
Patient Counselling. Definition of patient counseling; steps involved in pati...raviapr7
 
The Stolen Bacillus by Herbert George Wells
The Stolen Bacillus by Herbert George WellsThe Stolen Bacillus by Herbert George Wells
The Stolen Bacillus by Herbert George WellsEugene Lysak
 
Human-AI Co-Creation of Worked Examples for Programming Classes
Human-AI Co-Creation of Worked Examples for Programming ClassesHuman-AI Co-Creation of Worked Examples for Programming Classes
Human-AI Co-Creation of Worked Examples for Programming ClassesMohammad Hassany
 
In - Vivo and In - Vitro Correlation.pptx
In - Vivo and In - Vitro Correlation.pptxIn - Vivo and In - Vitro Correlation.pptx
In - Vivo and In - Vitro Correlation.pptxAditiChauhan701637
 
2024.03.23 What do successful readers do - Sandy Millin for PARK.pptx
2024.03.23 What do successful readers do - Sandy Millin for PARK.pptx2024.03.23 What do successful readers do - Sandy Millin for PARK.pptx
2024.03.23 What do successful readers do - Sandy Millin for PARK.pptxSandy Millin
 
UKCGE Parental Leave Discussion March 2024
UKCGE Parental Leave Discussion March 2024UKCGE Parental Leave Discussion March 2024
UKCGE Parental Leave Discussion March 2024UKCGE
 
Prescribed medication order and communication skills.pptx
Prescribed medication order and communication skills.pptxPrescribed medication order and communication skills.pptx
Prescribed medication order and communication skills.pptxraviapr7
 
Maximizing Impact_ Nonprofit Website Planning, Budgeting, and Design.pdf
Maximizing Impact_ Nonprofit Website Planning, Budgeting, and Design.pdfMaximizing Impact_ Nonprofit Website Planning, Budgeting, and Design.pdf
Maximizing Impact_ Nonprofit Website Planning, Budgeting, and Design.pdfTechSoup
 
HED Office Sohayok Exam Question Solution 2023.pdf
HED Office Sohayok Exam Question Solution 2023.pdfHED Office Sohayok Exam Question Solution 2023.pdf
HED Office Sohayok Exam Question Solution 2023.pdfMohonDas
 
How to Solve Singleton Error in the Odoo 17
How to Solve Singleton Error in the  Odoo 17How to Solve Singleton Error in the  Odoo 17
How to Solve Singleton Error in the Odoo 17Celine George
 
How to Make a Field read-only in Odoo 17
How to Make a Field read-only in Odoo 17How to Make a Field read-only in Odoo 17
How to Make a Field read-only in Odoo 17Celine George
 

Último (20)

Finals of Kant get Marx 2.0 : a general politics quiz
Finals of Kant get Marx 2.0 : a general politics quizFinals of Kant get Marx 2.0 : a general politics quiz
Finals of Kant get Marx 2.0 : a general politics quiz
 
Education and training program in the hospital APR.pptx
Education and training program in the hospital APR.pptxEducation and training program in the hospital APR.pptx
Education and training program in the hospital APR.pptx
 
The basics of sentences session 10pptx.pptx
The basics of sentences session 10pptx.pptxThe basics of sentences session 10pptx.pptx
The basics of sentences session 10pptx.pptx
 
Drug Information Services- DIC and Sources.
Drug Information Services- DIC and Sources.Drug Information Services- DIC and Sources.
Drug Information Services- DIC and Sources.
 
Patterns of Written Texts Across Disciplines.pptx
Patterns of Written Texts Across Disciplines.pptxPatterns of Written Texts Across Disciplines.pptx
Patterns of Written Texts Across Disciplines.pptx
 
CapTechU Doctoral Presentation -March 2024 slides.pptx
CapTechU Doctoral Presentation -March 2024 slides.pptxCapTechU Doctoral Presentation -March 2024 slides.pptx
CapTechU Doctoral Presentation -March 2024 slides.pptx
 
Benefits & Challenges of Inclusive Education
Benefits & Challenges of Inclusive EducationBenefits & Challenges of Inclusive Education
Benefits & Challenges of Inclusive Education
 
Diploma in Nursing Admission Test Question Solution 2023.pdf
Diploma in Nursing Admission Test Question Solution 2023.pdfDiploma in Nursing Admission Test Question Solution 2023.pdf
Diploma in Nursing Admission Test Question Solution 2023.pdf
 
Patient Counselling. Definition of patient counseling; steps involved in pati...
Patient Counselling. Definition of patient counseling; steps involved in pati...Patient Counselling. Definition of patient counseling; steps involved in pati...
Patient Counselling. Definition of patient counseling; steps involved in pati...
 
The Stolen Bacillus by Herbert George Wells
The Stolen Bacillus by Herbert George WellsThe Stolen Bacillus by Herbert George Wells
The Stolen Bacillus by Herbert George Wells
 
Human-AI Co-Creation of Worked Examples for Programming Classes
Human-AI Co-Creation of Worked Examples for Programming ClassesHuman-AI Co-Creation of Worked Examples for Programming Classes
Human-AI Co-Creation of Worked Examples for Programming Classes
 
In - Vivo and In - Vitro Correlation.pptx
In - Vivo and In - Vitro Correlation.pptxIn - Vivo and In - Vitro Correlation.pptx
In - Vivo and In - Vitro Correlation.pptx
 
Prelims of Kant get Marx 2.0: a general politics quiz
Prelims of Kant get Marx 2.0: a general politics quizPrelims of Kant get Marx 2.0: a general politics quiz
Prelims of Kant get Marx 2.0: a general politics quiz
 
2024.03.23 What do successful readers do - Sandy Millin for PARK.pptx
2024.03.23 What do successful readers do - Sandy Millin for PARK.pptx2024.03.23 What do successful readers do - Sandy Millin for PARK.pptx
2024.03.23 What do successful readers do - Sandy Millin for PARK.pptx
 
UKCGE Parental Leave Discussion March 2024
UKCGE Parental Leave Discussion March 2024UKCGE Parental Leave Discussion March 2024
UKCGE Parental Leave Discussion March 2024
 
Prescribed medication order and communication skills.pptx
Prescribed medication order and communication skills.pptxPrescribed medication order and communication skills.pptx
Prescribed medication order and communication skills.pptx
 
Maximizing Impact_ Nonprofit Website Planning, Budgeting, and Design.pdf
Maximizing Impact_ Nonprofit Website Planning, Budgeting, and Design.pdfMaximizing Impact_ Nonprofit Website Planning, Budgeting, and Design.pdf
Maximizing Impact_ Nonprofit Website Planning, Budgeting, and Design.pdf
 
HED Office Sohayok Exam Question Solution 2023.pdf
HED Office Sohayok Exam Question Solution 2023.pdfHED Office Sohayok Exam Question Solution 2023.pdf
HED Office Sohayok Exam Question Solution 2023.pdf
 
How to Solve Singleton Error in the Odoo 17
How to Solve Singleton Error in the  Odoo 17How to Solve Singleton Error in the  Odoo 17
How to Solve Singleton Error in the Odoo 17
 
How to Make a Field read-only in Odoo 17
How to Make a Field read-only in Odoo 17How to Make a Field read-only in Odoo 17
How to Make a Field read-only in Odoo 17
 

Foundation c2 exam june 2013 resit 2 sols

  • 1. Subtract 1 2 mark for reducible fractions or incorrect rounding. Question marks: 4, 7, 6, 15, 5, 11, 16, 9, 9,18 1. (a) Simplify 6x3 + 8y − 7x3 − 14y + 2x3 (2 marks) x3 − 6y 1 mark per term (b) Evaluate y3 x when y = 2 and x = 4. (2 marks) 23 4 = 8 4 = 2 2 marks soln, 1 mark working but incorrect soln 2. (a) What is the equation of the line passing through the point (4, 3) with gradient 1 2 ? (3 marks) 3 = 1 2 × 4 + c (1 mark) c = 1 (1 mark) y = 1 2 x + 1 (1 mark) (b) Solve the simultaneous equations (4 marks) x −2y = −2 x −y = −4 y = −2 (2 marks) x = −6 (2 marks) 3. A farmer keeps track of how many eggs his hens lay. 2 2 4 3 5 4 4 2 4 (a) What is the mode? (1 marks) Mode is 4. (b) What is the median? (2 marks) Ordered data: 2 2 2 3 4 4 4 4 5 9 × 1 2 = 4.5 Median=4 1 mark ordered table 1 mark median (c) What is the interquartile range? (3 marks) 9 × 1 4 = 2.25 Q1 = 2 (1 mark) 9 × 3 4 = 6.75 Q3 = 4 (1 mark) IQR= 4 − 2 = 2 (1 mark) 4. Sloths should have a mean of 16.5 hours sleep a day. A sloth owner wants to see if his sloths are sleeping too much and collects the following data. 17 18 20 19 16 (a) State the null hypothesis and the alternative hypothesis. (2 marks) H0 : µ = 16.5 H1 : µ > 16.5 1 mark for 16.5, 1 mark for >, -1 mark if no µ 1
  • 2. (b) What is the mean of the test data? (2 marks) µ(X) = 90 5 = 18 2 marks for correct soln, 1 mark if correct working incorrect sol (c) What is the sample standard deviation of the test data? (4 marks) σ2 (X) = 1630−5×182 4 = 2.5 σ(X) = 1.5811 1 mark sum of squares, 1 mark working, 1 mark sample var, 1 mark soln (d) What is the T test statistic? (3 marks) T = 18−16.5 1.5811/ √ 5 = 2.121 1 mark identifying vars, 1 mark working, 1 mark soln (e) The study is taken with a 1% level of significance. What is the critical T value? (2 marks) df = 5 − 1 = 4 (1 mark) 1%, 1 tail, df = 4 C = 3.747 (1 mark) (f) What can we deduce? (2 marks) 2.121 < 3.747 (1 mark) Accept H0 (1 mark) 5. Consider the following triangle. 34 60 h (a) What is the length h to 2 d.p.? (2 mark) sin(60) = h 3 (1 mark) h = 2.60 (1 mark) (b) What is the area of the triangle 1 d.p.? (3 marks) Right triangle: Area = 1 2 × 2.60 × 3 × sin(30) = 1.95 (1 mark) Left triangle:√ 42 − 2.602 = 3.04 Area = 1 2 × 3.04 × .2.60 = 3.95 (1 mark) Area= 3.04 + 3.95 = 7. (1 mark) 6. Solve the following quadratic equations using the method stated. No points will be awarded if another method is used. Leave answers in surd form. (a) 3x2 + 12x + 5 = 0. Solve by using the quadratic formula. (4 marks) a = 3, b = 12, c = 5 x = −12± √ 122−4×3×5 2×3 = −6± √ 21 3 1 mark identifying a,b,c, 1 mark working, 2 marks soln (b) x2 − x − 6 = 0. Solve by factorising. (2 marks) (x − 3)(x + 2) = 0 (1 mark) 2
  • 3. x = −2, 3 (1 mark) (c) x2 + 10x + 6 = 0. Solve by completing the square. (5 marks) (x + 5)2 − 25 + 6 = 0 (2 marks) (x + 5)2 = 19 (1 mark) x + 5 = √ 19 (1 mark) x = −5 ± √ 19 (1 mark) 7. A researcher wants to show that height and baldness are independent. He collects the following data; Short Average Tall Luxuriant 6 6 8 Thinning 7 8 5 Bald 2 16 2 (a) State the null hypothesis and the alternative hypothesis. (2 marks) H0 : There is no correlation. (1 mark) H1 : there is a correlation. (1 mark) 1 mark if reversed (b) What is the χ2 test statistic? (10 marks) Totals: Short Average Tall Row total Luxuriant 6 6 8 20 Thinning 7 8 5 20 Bald 2 16 2 20 Column total 15 30 15 60 Fit: 5 10 5 5 10 5 5 10 5 Residual: 1 -4 3 2 -2 0 -3 6 -3 χ2 table: 0.2 1.6 1.8 0.8 0.4 0 1.8 3.6 1.8 χ2 = 12 2 marks per table, −1 2 per error, −1 2 per table with rounding errors, 2 marks for soln (c) If we test at a 5% level of significance what is the critical χ2 value? (2 marks) df = (3 − 1)(3 − 1) = 4 (1 mark) C = 9.49 (1 mark) (d) What can we deduce? (2 marks) 9.49 < 12 (1 mark) Reject H0. (1 mark) 3
  • 4. 8. (a) Show that there is a solution to x6 − 5x + 2 = 0 for some x between 0 and 1. (3 marks) Set f(x) = x6 − 5x + 2 f(0) = 2 (1 mark) f(1) = −2 (1 mark) f(0) > 0, f(1) < 0 so there is a soln to f(x) = 0 for some x between 0 and 1. (1 mark) (b) Use trial and improvement to find a solution to 1 d.p. (6 marks) x f(x) Soln between 0.5 -0.48 0 and 0.5 0.3 0.5 0.3 and 0.5 0.4 0.004 0.4 and 0.5 0.45 -0.24 0.4 and 0.45 Soln is 0.4 to 1 d.p. 3 marks working, 1 mark midpoint, 2 marks soln 9. An airship has speed v = 4t − 100t−2 . (a) What is the speed of the airship when t = 10? (1 mark) v(10) = 4 × 10 − 100 × 10−2 = 39 (b) What is the airships acceleration as a function of time? (3 marks) a = dv dt = 4 + 200t−3 1 mark differentiating, 1 mark per term (c) When t = 10 the distance x = 262. Write the distance the rocket travels as a function of time. (5 marks) x = vdt = 4t − 100t−2 dt = 2t2 + 100t−1 + C 262 = 2 × 102 + 100 × 10−1 + C C = 52 x = 2t2 + 100t−1 + 52 2 marks for integrating, 1 mark for substituting, 1 mark for c, 1 mark for soln 10. (a) Differentiate y = 8x3 − 2x. (2 marks) dy dx = 24x2 − 2 1 mark per term (b) What are the x and y co-ordinates of the stationary points of the graph y = 8x3 − 2x? (4 marks) dy dx = 0 24x2 − 2 = 0 x2 = 1 12 x = ± 1√ 12 = ±0.29 (2 marks) y( 1√ 12 ) = − 4 3 √ 12 = −0.38 (1 mark) y(− 1√ 12 ) = 4 3 √ 12 = 0.38 (1 mark) (c) What are the natures of these stationary points? (3 marks) d2 y dx2 = 48x (1 mark) d2 y dx2 ( 1√ 12 ) = 4 √ 12 > 0 Minimum (1 mark) d2 y dx2 (− 1√ 12 ) = −4 √ 12 < 0 Maximum (1 mark) 4
  • 5. (d) Sketch the graph y = 8x3 − 2x making sure to label your sketch clearly. (5 marks) −0.5 −0.29 0.29 0.5 −0.38 0.38 x y 1 mark per stat point, 2 marks for intercepts, 1 mark for shape (e) By integrating, find the area under the graph y = 8x3 − 2x between the values x = −0.5 and x = 0.5. (4 marks) 0.5 −0.5 8x3 − 2xdx = [2x4 − x2 ]0.5 −0.5 = (2 × 0.54 − 0.52 ) − (2 × (−0.5)4 − (−0.5)2 ) = 0 2 marks integral, 1 mark subs, 1 mark soln 5
  • 6. Formulae Let X be a list of data of size n. Mean: µ(X) = n i=1 X[i] n Variance σ2 (X) = n i=1(X[i])2 n − µ2 (X) Z-statistic Z = µ(X) − µ σ/ √ n Sample Variance σ2 (X) = n i=1(X[i])2 − nµ2 (X) n − 1 T-statistic T = µ(X) − µ σ(X)/ √ n Alternative notation Mean ¯x = x n Variance V ar = x2 n − ¯x2 Z-statistic Z = ¯x − A σ/ √ n Sample Variance s2 = x2 − n¯x2 n − 1 T-statistic T = ¯x − A s/ √ n 6
  • 7. Pythagoras’ Theorem a2 + b2 = c2 tan(A) = opp adj , cos(A) = adj hyp , sin(A) = opp hyp Sine rule a sin(A) = b sin(B) = c sin(C) Cosine rule a2 = b2 + c2 − 2bc cos(A) Area Area = 1/2ab sin(C) Quadratic formula x = −b ± √ b2 − 4ac 2a Equation of a straight line y = mx + c Gradient of a straight line m = y2 − y1 x2 − x1 χ2 Process 1. We refer to the entry in the ith column and the jth row as M(i, j). 2. Calculate the row totals Ri, the column totals Ci and the overall total T. 3. Construct the fit table. The entry in the ith column and jth row is given by: F(i, j) = Ci × Rj T 4. Construct the residual table. The entry in the ith column and jth row is given by: R(i, j) = M(i, j) − F(i, j) 5. Construct the χ2 -table. The entry in the ith column and jth row is given by: χ2 (i, j) = R(i, j)2 F(i, j) 7
  • 8. Tables Critical Z-values Sig. Lev. 5% Sig. Lev. 1% One-tail Two-tail One-tail Two-tail Probability 0.05 0.025 0.01 0.005 Critical value 1.65 1.96 2.33 2.58 Critical T-values Sig. Lev. 5% Sig. Lev. 1% One-tail Two-tail One-tail Two-tail d.f. 0.05 0.025 0.01 0.005 1 6.314 12.706 31.821 63.656 2 2.920 4.303 6.965 9.925 3 2.353 3.182 4.541 5.841 4 2.132 2.776 3.747 4.604 5 2.015 2.571 3.365 4.032 6 1.943 2.447 3.143 3.707 7 1.895 2.365 2.998 3.499 8 1.860 2.306 2.896 3.355 9 1.833 2.262 2.821 3.250 10 1.812 2.228 2.764 3.169 Critical χ2 value 5% significance 1% Significance df Probability 0.05 Probability 0.01 1 3.84 6.63 2 5.99 9.21 3 7.81 11.3 4 9.49 13.3 5 11.1 15.1 6 12.6 16.8 7 14.1 18.5 8 15.5 20.1 9 16.9 21.7 10 18.3 23.2 11 19.7 24.7 12 21.0 26.2 8