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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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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
Key Outcome Grade Facility Disc. Calculator Content Source
A 1.1 C 0 0 NC G2 2011 P1 Q8
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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
Key Outcome Grade Facility Disc. Calculator Content Source
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
Key Outcome Grade Facility Disc. Calculator Content Source
B 1.2 C 0 0 CN A5 2010 P1 Q5
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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
Key Outcome Grade Facility Disc. Calculator Content Source
B 1.2 C 0 0 NC A7 2009 P1 Q10
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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
Key Outcome Grade Facility Disc. Calculator Content Source
A 1.2 C 0 0 CN T4 2010 P1 Q4
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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 .
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 1.3 C 0 0 NC A2, C7 2012 P1 Q18
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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
Key Outcome Grade Facility Disc. Calculator Content Source
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.
Which of the following is true?
A. Neither statement is correct.
B. Only statement (1) is correct.
C. Only statement (2) is correct.
D. Both statements are correct. 2
Key Outcome Grade Facility Disc. Calculator Content Source
C 1.3 C 0 0 CN C4, C7 2010 P1 Q15
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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
Key Outcome Grade Facility Disc. Calculator Content Source
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
Key Outcome Grade Facility Disc. Calculator Content Source
C 1.3 C 0 0 NC C6 2009 P1 Q20
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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
Key Outcome Grade Facility Disc. Calculator Content Source
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
Key Outcome Grade Facility Disc. Calculator Content Source
C 1.4 C 0 0 NC A13 2010 P1 Q7
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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
Key Outcome Grade Facility Disc. Calculator Content Source
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.
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 2.1 A/B 0 0 NC A17 2011 P1 Q9
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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
Key Outcome Grade Facility Disc. Calculator Content Source
D 2.1 C 0 0 CN A18 2010 P1 Q6
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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
Key Outcome Grade Facility Disc. Calculator Content Source
D 2.1 C 0 0 NC A19 2012 P1 Q13
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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
Key Outcome Grade Facility Disc. Calculator Content Source
B 2.2 C 0 0 NC C16 2009 P1 Q16
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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
Key Outcome Grade Facility Disc. Calculator Content Source
B 2.3 C 0 0 NC T7 2009 P1 Q11
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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
Key Outcome Grade Facility Disc. Calculator Content Source
C 2.3 C 0 0 NC T9 2011 P1 Q12
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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
Key Outcome Grade Facility Disc. Calculator Content Source
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
Key Outcome Grade Facility Disc. Calculator Content Source
D 3.1 C 0 0 NC G16, G18 2012 P1 Q15
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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
Key Outcome Grade Facility Disc. Calculator Content Source
B 3.1 C 0 0 NC G22, G21 2012 P1 Q10
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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
Key Outcome Grade Facility Disc. Calculator Content Source
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
Key Outcome Grade Facility Disc. Calculator Content Source
C 3.2 C 0 0 NC C20, T3 2011 P1 Q13
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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
Key Outcome Grade Facility Disc. Calculator Content Source
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
Key Outcome Grade Facility Disc. Calculator Content Source
A 3.2 C 0 0 NC C22 2012 P1 Q14
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28. Simplifylogb 9a
2
logb 3a, where a > 0 and b > 0.
A. 2
B. 3a
C. logb 3a
D. logb(9a2 − 3a) 2
Key Outcome Grade Facility Disc. Calculator Content Source
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
Key Outcome Grade Facility Disc. Calculator Content Source
B 3.4 C 0 0 NC T12 2009 P1 Q13
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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
Key Outcome Grade Facility Disc. Calculator Content Source
D 1.2 C 0 0 NC A4, T3 2010 P1 Q11
[END OF QUESTIONS]
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