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Higher Still
Intermediate 2
Mathematics 3
Practice Unit Test 1
Practice Unit Test 2
Practice Unit Test 3
Answers
2
 Pegasys 2003
Mathematics 3 (Int2)
Practice Unit Assessment 1
Mathematics 3 (Int2)
Outcome 1
Q1.
Express in its simplest form
Q2.
Simplify :
5 2

a.
a a
( y  7)( y  2)
( y  7) 2
3 4

c d
b.
c.
Q3.
Change the subject of this formula to x :
Q4.
Simplify :
a.
Q5.
Simplify :
a.
18
x
5
x y

3w 4
d.
a c

2b 5
w = 5x  y
b.
x3  x4
,y7
b.
36
49
5c8  3c3
Outcome 2
Q6.
y
(2,20)
Write down the equation of the quadratic function
shown in the diagram of the form y = ax2.
(1, 5)
0
Q7.
x
y
Write down the equation of the function shown opposite
which is of the form y = (x + a)2 + b.
x
0
(3,4)
Q8.
The equation of a quadratic function is y = (x + 5)2 + 1.
a.
Write down the equation of the axis of symmetry.
b.
Write down the coordinates of the turning point and say whether it is a
maximum or a minimum.
 Pegasys 2003
Mathematics 3 (Int2)
Q9.
Use the graph shown to solve the equation
2
y
x2 + x – 6 = 0.
4
2
0
2
4
x
2
4
6
Q10. Factorise and solve x2  8x + 12 = 0
Q11. Solve the equation
x2 + 10x  5 = 0 using the quadratic formula.
Outcome 3
Q12. Sketch the graph of y = cos xo
for 0  x  360.
y
Q13. The diagram shows the graph of y = sin axo.
1
Write down the value of a.
0
90
180
270
360
1
Q14. Solve the equation 2 sinxo  1 = 0, 0  x  360.
End of Unit Assessment
 Pegasys 2003
Mathematics 3 (Int2)
xo
Practice Unit Assessment 2
Mathematics 3 (Int2)
Outcome 1
Q1.
Express in its simplest form
Q2.
Simplify :
7 3

a.
m m
(d  4)(d  3)
(d  4) 2
2 5

a b
b.
Q3.
Change the subject of this formula to x :
Q4.
Simplify :
a.
Q5.
Simplify :
a.
32
x
3
3w y

x 5
c.
3p r

q 2
d.
w = px  7
b.
x6  x5
, d  4.
b.
64
9
3c5  6c2
Outcome 2
Q6.
y
(2, 12)
Write down the equation of the quadratic function
shown in the diagram of the form y = ax2.
(1,3)
0
Q7.
x
Write down the equation of the function shown opposite
which is of the form y = (x + a)2 + b.
y
(1,6)
x
0
Q8.
The equation of a quadratic function is y = (x  5)2  2.
a.
Write down the equation of the axis of symmetry.
b.
Write down the coordinates of the turning point and say whether it is a
maximum or a minimum.
 Pegasys 2003
Mathematics 3 (Int2)
Q9.
Use the graph shown to solve the equation
2
y
x2 + 3x – 4 = 0.
4
2
0
2
4
x
2
4
6
Q10. Factorise and solve x2  6x + 8 = 0
Q11. Solve the equation
x2 + 11x  15 = 0 using the quadratic formula.
Outcome 3
Q12. Sketch the graph of y = 2cos xo
for 0  x  360.
Q13. The diagram shows the graph of y = sin axo.
y
1
Write down the value of a.
0
90
180
270
360
1
Q14. Solve the equation 3 cosxo  2 = 0, 0  x  360.
End of Unit Assessment
 Pegasys 2003
Mathematics 3 (Int2)
xo
Practice Unit Assessment 3
Mathematics 3 (Int2)
Outcome 1
Q1.
Express in its simplest form
Q2.
Simplify :
9 5

a.
p p
(m  5)(m  2)
(m  2) 2
8 11

y x
b.
Q3.
Change the subject of this formula to x :
Q4.
Simplify :
Q5.
a.
Simplify :
a.
24
a
2
c a

3d 4
c.
x 6

y w
d.
w = cx + d
b.
a3  a4
, m  2.
b.
36
25
3x3  5x7
Outcome 2
Q6.
y
(4, 32)
Write down the equation of the quadratic function
shown in the diagram of the form y = ax2.
(2, 8)
0
Q7.
x
Write down the equation of the function shown opposite
which is of the form y = (x + a)2 + b.
y
(2,5)
x
0
Q8.
The equation of a quadratic function is y = (x  7)2 + 8.
a.
Write down the equation of the axis of symmetry.
b.
Write down the coordinates of the turning point and say whether it is a
maximum or a minimum.
 Pegasys 2003
Mathematics 3 (Int2)
Q9.
y
Use the graph shown to solve the equation
6
x2 + 3x – 4 = 0.
4
2
4
2
0
2
4
x
2
Q10. Factorise and solve x2  8x + 15 = 0
Q11. Solve the equation
x2  5x  9 = 0 using the quadratic formula.
Outcome 3
Q12. Sketch the graph of y = 2sin xo
for 0  x  360.
Q13. The diagram shows the graph of y = cos axo.
y
1
Write down the value of a.
0
90
180
270
360
1
Q14. Solve the equation 4 sinxo  1 = 0, 0  x  360.
End of Unit Assessment
 Pegasys 2003
Mathematics 3 (Int2)
xo
Answers
Practice Unit Assessment 1
y2
1.
y7
3
3d  4c
xy
5a
2.
a.
b.
c.
d.
a
cd
12 w
2bc
1
3.
x = /5 (w + y)
4.
a. 3 2 b. 6/7
5.
a. x2
b. 15c5
6.
y = 5x2
7.
y = (x  3)2  4
8.
a. x = 5 b. (5, 1) Min
9.
x = 3 or 2
10.
(x  2)(x  6); x = 2, x = 6
11.
x =  10.48 or 0.48
12.
graph of y = cos xo, 0 x 360
13.
a=3
14.
x = 30o or 150o
M3 (Int2)
Practice Unit Assessment 2
d 3
1.
d 4
6p
4
2b  5a
3wy
2.
a.
b.
c.
d.
m
ab
5x
qr
1
3.
x = /p (w + 7)
4.
a. 4 2 b. 8/3
5.
a. x8
b. 18c3
6.
y = 3x2
7.
y = (x  1)2 + 6
8.
a. x = 5 b. (5, 2) Min
9.
x = 4 or 1
10.
(x  2)(x  4) ; x = 2, x = 4
11.
x =  12.2 or 1.2
12.
graph of y = 2cos xo, 0 x 360
13.
a=2
14.
x = 48.2o or 311.8o
Practice Unit Assessment 3
m5
1.
m2
14
wx
8 x  11y
ac
2.
a.
b.
c.
d.
12d
p
xy
6y
3.
x = 1/c (w  d)
4.
a. 2 6 b. 6/5
5.
a. a5
b. 15x4
6.
y = 2x2
7.
y = (x  2)2 + 5
8.
a. x = 7 b. (7, 8) Min
9.
x = 1 or 4
10.
(x  3)(x  5) ; x = 3, x = 5
11.
x =  1.4 or 6.4
12.
graph of y = 2sin xo, 0 x 360
13.
a=4
14.
x = 14.5o or 165.5o
 Pegasys 2003
Mathematics 3 (Int2)