VECTORS
1.The distance between P and Q is
A.
B.7
C.
D.
2. and . The value of is
A.17
B.13
C.8
D.7
3.The point R divides EF in the ratio 2 : 3. If E is the point and F is , the
coordinates of R are
A.
B.
C.
D.
4.The vectors and are perpendicular. The value of a is A.
B.15
C.
D.45
5.Two vectors are defined as and . The cosine of the angle between them is
A.
B.
C.
D.
6.X is the point , Y is and Z is . If X, Y and Z are collinear, the value of b is
A.3
B.
C.7
D.23
7.A is the point and B is . The point C divides AB in the ratio 1 : 4. The
coordinates of C are
A.
B.
C.
D.
8.Given that , and = 7, the value of a.() is
A.15
B.35
C.16
D.49
9.The length of vector a defined as is
A.2
B.6
C.
D.
10.The vectors and are parallel. The value of x is
A.
B.6
C.
D.625
11.The vectors and are perpendicular. The value of x is
A.
B.
C.
D.24
12.A is the point (2, 3, 6), B is (4, 5, 8) and C(8, 9, 12). B divides AC in the ratio
A.1 : 2
B.2 : 1
C.3 : 1
D.1 : 3
13.A is the point (6, 1, 7) and B is . The point K divides AB in the ratio 4 : 1. The
coordinates of K are
A.
B.
C.
D.
14.P is the point and Q is (3, 1, 3). The components of PQ are
A.
B.
C.
D.
15.
The value of a . b is
A.6
B.
C.
D.
CALCULUS
1.equals
A.
B.
C.
D.
2. equals
A.
B.
C.
D.
3.If , equals
A.
B.
C.
D.
4. 4cos 2x dx equals
A.
B.
C.
D.
5. equals
A.
B.
C.
D.
6.Given that , equals
A.1
B.3
C.0
D.-3
7. equals
A.
B.
C.
D.
8. equals
A.
B.
C.2
D.
9.If , equals
A.
B.
C.
D.
10. equals
A.
B.
C.
D.
11.The rate of change of the function at the point where is
A.
B.
C.
D.
12.The value of cosxdx is
A.1
B.
C.2
D.0
13.
A.
B.
C.
D.
14., equals
A.
B.
C.
D.
15., equals
A.
B.
C.
D.
16. equals
A.
B.
C.
D.
17.A curve has equation . The gradient of the tangent to this curve at the point is
A.0
B.3
C.
D.
18. equals
A.
B.
C.
D.
19. equals
A.
B.
C.
D.
20.If
A.
B.
C.
D.
21. equals
A.
B.
C.
D.
22.equals
A.
B.
C.
D.
23.The gradient of the tangent to the curve at the point with x-coordinate is
A.
B.1
C.
D.
24. equals
A.
B.
C.
D.
25. equals
A.
B.
C.
D.
26.The area between the graphs of and y = 9 is found from
A.
B.
C.
D.
27. The value of is
A.
B.
C.
D.
28. equals
A.
B.
C.
D.
29. equals
A.
B.
C.
D.
30., equals
A.
B.
C.
D.
LOGARITHMS and EXPONENTIALS
1.in logarithmic form is
A.
B.
C.
D.
2.The value of is
A.2
B.
C.
D.
3.If the value of x is
A.25
B.
C.32
D.10
4. expressed as a single logarithm is
A.
B.
C.
D.
5.. The value of a is
A.
B.3
C.8
D.16
6.The diagram shows the graph of
A.
B.
C.
D.
7.A sketch of the graph of is shown in the diagram.
The values of a and b are
A.a = 3 and b = 5
B.a = 3 and b = 2
C.a = and b = 5
D.a = and b = 2
8.The value of n is
A.6
B.7
C.64
D.128
9.The graph of is shown as a broken line in the diagram.
The equation of the graph shown as a full line is
A.
B.
C.
D.
10.The value of is
A.3
B.4
C.8
D.16
11. expressed as a single logarithm is
A.
B.
C.
D.
12.The value of is
A.1
B.2
C.8
D.4
13.Expressing as a single logarithm is
A.
B.
C.
D.
14.The graph of crosses the x-axis at the point where x equals
A.1
B.0
C.
D.5
15.The value of is
A.
B.2
C.
D.
16.When is simplified, the answer is
A.0
B.
C.1
D.
17.The value of is
A.1
B.33
C.6
D.5
18.Given that then value of x is
A.
B.12
C.81
D.64
19.The graph of crosses the x-axis at the point
A.
B.0
C.5
D.
20.The graph of is shown by the full line in the diagram
The broken line shows the graph of a related function.
The related graph has equation
A.
B.
C.
D.
THE WAVE FUNCTION
1.The maximum value of occurs where x equals
A.120o
B.90o
C.60o
D.30o
2.The minimum value of occurs where x equals
A.30o
B.150o
C.210o
D.300o
3.The maximum value of is
A.
B.1
C.2
D.
4.If and , the values of k and tan are
A.and
B.and
C.and
D.and
5.The maximum value of occurs where x equals
A.130o
B.40o
C.320o
D.50o
6.The minimum value of occurs where x equals
A.220o
B.310o
C.40o
D.130o
7.The maximum value of is
A.2
B.3
C.
D.5
8.The maximum value of is
A.7
B.
C.3
D.4
9.Given that and , the values of k and are
A.
B.
C.
D.
10.When is expressed in the form , the values of k andis
A.
B.
C.
D.
11.The solution of the equation
A.
B.
C.
D.
12.The maximum and minimum values of are
Maximum / MinimumA / 7 / 3
B / 5 / -5
C / 2 / -2
D / 5 / 3
13.If and , (0 < x < 360) the values of k and are
A.
B.
C.
D.
14.When is expressed in the form the values of k and tanare
A.
B.
C.
D.
15.The maximum and minimum values of are
Maximum / MinimumA / 2 /
B / 5 /
C / 2 / 0
D / 3 / 0
MIXED EXERCISE - UNIT 3
1.A is the point and B is(. The value of a . b is
A.17
B.
C.8
D.16
2.When is expressed as the log of a single numbers it equals
A.log 15
B.log 5
C.log 1
D.log 6
3.equals
A.
B.
C.
D.
4.The diagram shows the graph of .
The point (4, 1) lies on the graph. The value of b is
A.
B.4
C.1
D.0
5. equals
A.
B.
C.
D.
6.The minimum value of occurs where x equals
A.60o
B.120o
C.240o
D.300o
7.expressed as a single log is
A.
B.
C.
D.
8. equals
A.
B.
C.
D.
9.The graph shown has equation .
The values of a and b are
A. and
B. and
C. and
D.and
10.)equals
A.
B.
C.
D.
11.A is the point and B is the point . C divides AB in the ratio 3 : 2. The
coordinates of C are
A.
B.
C.
D.
12. equals
A.
B.
C.
D.
13.The three sides, each of length 3 units, of an equilateral triangle are
represented by p, q and r as shown in the diagram.
The value of p . (p + q) is
A.0
B.18
C.
D.
14.equals
A.
B.
C.
D.
15.The maximum value of and the value of x (at which it occurs are
A.4 when
B.4 when
C.3 when
D.3 when
16. equals
A.
B.
C.
D.
17.The angle between a and b is 60o. and . The value of a . b is
A.
B.3
C.
D.
18.Given that, equals
A.
B.
C.
D.12x
19.equals
A.
B.
C.
D.
20.The minimum value of is
A.
B.
C.17
D.9
Pegasys 2008 Higher Mathematics - Unit 3