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Higher Mathematics

Exam Revision 5(multiple choice)

1. Here are two statements about the points S(2, 3) and T(5,−1) :

I. The length of ST = 5 units;

II. The gradient of ST = 43 .

Which of the following is true?

A. neither statement is correct

B. only statement I is correct

C. only statement II is correct

D. both statements are correct 2

Key Outcome Grade Facility Disc. Calculator Content Source

B 1.1 C 0 0 NC G1, G2 2009 P1 Q5

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Higher Mathematics

2. A line makes an angle of 30◦ with the positive direction of the x -axis as shown.

30°

O x

y

What is the gradient of the line?

A. 1√3

B. 1√2

C. 12

D.√32 2


A 1.1 C 0 0 NC G2 2011 P1 Q8

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Higher Mathematics

3. If f (x) = 2 sin(

3x− π

2

)

+ 5, what is the range of values of f (x)?

A. −1 ≤ f (x) ≤ 11

B. 2 ≤ f (x) ≤ 8

C. 3 ≤ f (x) ≤ 7

D. −3 ≤ f (x) ≤ 7 2


C 1.2 C 0 0 NC A1 2009 P1 Q14

4. When x2 + 8x+ 3 is written in the form (x+ p)2 + q , what is the value of q?

A. −19

B. −13

C. −5

D. 19 2


B 1.2 C 0 0 CN A5 2010 P1 Q5

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Higher Mathematics

5. Which of the following graphs has equation y = log5(x− 2)?

A.

(3, 1)

(–1, 0)

O x

y

B.

(7, 1)

(3, 0)O x

y

C.

(1, 7)

(0, 3)

O x

y

D.

(1, 7)

(7, 1)

O x

y

2


B 1.2 C 0 0 NC A7 2009 P1 Q10

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Higher Mathematics

6. The diagram shows the graph with equation of the form y = a cos bx for0 ≤ x ≤ 2π .

2

π 2π

–2

O x

y

What is the equation of this graph?

A. y = 2 cos 3x

B. y = 2 cos 2x

C. y = 3 cos 2x

D. y = 4 cos 3x 2


A 1.2 C 0 0 CN T4 2010 P1 Q4

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Higher Mathematics

7. The graph of y = f (x) shown has stationary points at (0, p) and (q, r) .

= f( )

(q, r)

s t

p

O x

xyy

Here are two statements about f (x) :

I. f (x) < 0 for s < x < t ;

II. f ′(x) < 0 for x < q .







B 1.3 C 0 0 NC A2, C7 2012 P1 Q18

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Higher Mathematics

8. If y = 3x−2+ 2x32 , x > 0, determine

dydx .

A. −6x−3 + 45x52

B. −3x−1 + 3x12

C. −6x−3 + 3x12

D. −3x−1 + 45x52 2


C 1.3 C 0 0 NC C1, C2 2012 P1 Q6

9. The derivative of a function f is given by f ′(x) = x2 − 9.Here are two statements about f :

(1) f is increasing at x = 1;

(2) f is stationary at x = −3.


A. Neither statement is correct.

B. Only statement (1) is correct.

C. Only statement (2) is correct.

D. Both statements are correct. 2


C 1.3 C 0 0 CN C4, C7 2010 P1 Q15

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Higher Mathematics

10. If s(t) = t2 − 5t+ 8, what is the rate of change of s with respect to t when t = 3?A. −5

B. 1

C. 2

D. 9 2


B 1.3 C 0 0 NC C6 2010 P1 Q17

11. A = 2πr2 + 6πr

What is the rate of change of A with respect to r when r = 2?

A. 10π

B. 12π

C. 14π

D. 20π 2


C 1.3 C 0 0 NC C6 2009 P1 Q20

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Higher Mathematics

12. A sequence is defined by the recurrence relation un+1 = 3un + 4, with u0 = 1.

Find the value of u2 .

A. 7

B. 10

C. 25

D. 35 2


C 1.4 C 0 0 NC A11 2012 P1 Q1

13. A sequence is generated by the recurrence relation un+1 = 14un + 7, with

u0 = −2.What is the limit of this sequence as n→ ∞?

A. 128

B. 285

C. 283

D. 28 2


C 1.4 C 0 0 NC A13 2010 P1 Q7

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Higher Mathematics

14. What is the solution of x2+ 4x > 0, where x is a real number?

A. −4 < x < 0

B. x < −4, x > 0

C. 0 < x < 4

D. x < 0, x > 4 2


B 2.1 C 0 0 CN A16 2010 P1 Q18

15. The discriminant of a quadratic equation is 23.

Here are two statements about this quadratic equation:

I. the roots are real;

II. the roots are rational.







B 2.1 A/B 0 0 NC A17 2011 P1 Q9

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Higher Mathematics

16. The roots of the equation kx2 − 3x+ 2 = 0 are equal.

What is the value of k?

A. − 98B. − 89C. 8

9

D. 98 2


D 2.1 C 0 0 CN A18 2010 P1 Q6

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Higher Mathematics

17. A parabola intersects the axes at x = −2, x = −1 and y = 6, as shown in thediagram.

–2

6

–1 O x

y

What is the equation of the parabola?

A. y = 6(x− 1)(x− 2)

B. y = 6(x+ 1)(x+ 2)

C. y = 3(x− 1)(x− 2)

D. y = 3(x+ 1)(x+ 2) 2


D 2.1 C 0 0 NC A19 2012 P1 Q13

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Higher Mathematics

18. The graph of y = 4x3 − 9x2 is shown in the diagram.Which of the following gives the area of the shaded section?

O 1

–5

= 43

– 92xx

x

yy

A.[

x4 − 3x3]0

−5

B. −[

x4 − 3x3]1

0

C.[

12x2 − 18x]0

−5

D. −[

12x2 − 18x]1

02


B 2.2 C 0 0 NC C16 2009 P1 Q16

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Higher Mathematics

19. How many solutions does the equation

(4 sin x−√5)(sin x+ 1) = 0

have in the interval 0 ≤ x < 2π?

A. 4

B. 3

C. 2

D. 1 2


B 2.3 C 0 0 NC T7 2009 P1 Q11

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Higher Mathematics

20. The diagram shows two right-angled triangles with sides and angles as given.

2

3

2

pq

1

5

What is the value of sin(p+ q)?

A. 2√5+ 23

B. 2√5+

√53

C. 23 + 2

3√5

D. 43√5+ 13 2


C 2.3 C 0 0 NC T9 2011 P1 Q12

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Higher Mathematics

21. The point P(2,−3) lies on the circlewith centre C as shown.The gradientof CP is −2.What is the equation ofthe tangent at P?

C

P(2, –3)

O x

y

A. y+ 3 = −2(x− 2)

B. y− 3 = −2(x+ 2)

C. y+ 3 = 12(x− 2)

D. y− 3 = 12(x+ 2) 2


C 2.4 C 0 0 NC G11 2011 P1 Q6

22. If u = k

3−10

, where k > 0 and u is a unit vector, determine the value of k .

A. 12

B. 18

C. 1√2

D. 1√10

2


D 3.1 C 0 0 NC G16, G18 2012 P1 Q15

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Higher Mathematics

23. The diagram shows a square-based pyramid P,QRST.−→TS,

−→TQ and

−→TP represent f ,

g and h respectively.

R

T

P

S

Q

f

h

g

Express−→RP in terms of f , g and h .

A. − f + g − h

B. − f − g + h

C. f − g − h

D. f + g + h 2


B 3.1 C 0 0 NC G22, G21 2012 P1 Q10

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Higher Mathematics

24. If u =

−312t

and v =

1t−1

are perpendicular, what is the value of t?

A. −3

B. −2

C. 23

D. 1 2


A 3.1 C 0 0 NC G27 2012 P1 Q7

25. Given that f (x) = 4 sin 3x , find f ′(0) .

A. 0

B. 1

C. 12

D. 36 2


C 3.2 C 0 0 NC C20, T3 2011 P1 Q13

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Higher Mathematics

26. If y = 3 cos4 x , finddydx .

A. 12 cos3 x sin x

B. 12 cos3 x

C. −12 cos3 x sin x

D. −12 sin3 x 2


C 3.2 C 0 0 NC C21, C23 2012 P1 Q16

27. Find∫

(2x− 1)12 dx where x >

12 .

A. 13(2x− 1)

32 + c

B. 12(2x− 1)−

12 + c

C. 12(2x− 1)

32 + c

D. 13(2x− 1)−

12 + c 2


A 3.2 C 0 0 NC C22 2012 P1 Q14

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Higher Mathematics

28. Simplifylogb 9a

2

logb 3a, where a > 0 and b > 0.

A. 2

B. 3a

C. logb 3a

D. logb(9a2 − 3a) 2


A 3.3 A/B 0 0 NC A28 2012 P1 Q20

29. k and a are given by

k sin a◦ = 1

k cos a◦ =√3

where k > 0 and 0 ≤ a < 90.

What are the values of k and a?

k a

A. 2 60

B. 2 30

C.√10 60

D.√10 30

2


B 3.4 C 0 0 NC T12 2009 P1 Q13

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Higher Mathematics

30. Functions f and g are defined on suitable domains by f (x) = cos x andg(x) = x+ π

6 .

What is the value of f(

g(

π

6

))

?

A. 12 + π

6

B.√32 + π

6

C.√32

D. 12 2


D 1.2 C 0 0 NC A4, T3 2010 P1 Q11

[END OF QUESTIONS]

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