R
E
D
15-4-15
Answers
Straight Line Graphs Solutions
1.
y = -6
2.
a:y= 5x – 3
c:y= 3x, y=5 + 3x
3.
Graph A
y= 2x+1
Graph C
y= 2x – 3
Graph E
y= 5
4.
b) (2,5) because 3x2 – 1 = 5
d) (-2,-7) because 3x-2 – 1 = -7
5. a)
x
-3
-2
-1
y
-9
-7
-5
c)
0
-3
1
-1
y= 2x +3
y=
3x
y= ½x + 1
y= 5 – ½x
2
1
3
3
i)When x = 1.7 y=0.4
ii)
When y=-4.3, x = -0.65
Area and perimeter
1) 2.5 cm by 8cm
2)
b:d:Graph B
Graph D
4cm by 11 cm
area = 20 cm2
Perimeter = 21 cm
area = 22 cm2
3) area = ½ x 3 x 5.2
area = 7.8 mm2
4)
AREA = ½ x 10 x 3.3
5)
area
perimeter = 14.2 mm
= 16.5 mm2
= ½x12x10 - 3x2
= 60 – 6
= 54 m2
Fractions and decimals
1)
2)
0.09876 , 0.1 , 0.25 , 0.4 , 0.99
⅛ , ⅜ , ⅝ , ⅞
3)0.3, ⅜, 0.45, 0.5, ⅝
4) (a) 0.2 (b) 0.6666… (c) 6.25
5) (a)
6) (a) 0.21
7)
(b) 0.12845
1
3
4
7
(b) 12
/5 of five million pounds
8) (a) 80 + 4 x 260 = £1120
(b)
2
33
(c)
1800 – 600 -300 = £900
15 minutes for 15 days
R
E
Simplify, expand and factorise
D
1. 7x
15-4-15
2. 3a + 5b
3. 15c – 6d
4. 12e – 4f + 7e + 14f = 19e + 10f
5. 4(3c + 2d)
6. 7(2e – f)
7. 15e – 6f – 8e – 4f = 7e – 10f
8. 12e – 18f – 10e + 20f = 2e + 2f
9. y2 + 3y
10. 8y2 – 6y
11. x(x – 5)
12. 3x(2x + 1)
13. 5q2(1 – 3q)
14. x2 + 7x + 12
2
15. 3x - 13x – 10
Measures and conversions
1. 310
2.
500
3.
(a)1 m2
4.
50000 cm2
5. a) 5000000 cm3
6. 7.5 cm
8. 8 km
Percentages
1
80%……
4
5.
7a
B
(b)
b)
2
10000 cm2
5000 l
7.
9.
6.6 lbs
£2.78
…£20…….
3
…£70….
20
90 x 4
20%
+ %
45 = 405
6.
11
11 %
…405…
207 ÷ 9 out of 100
…23%...
Prime numbers and factors
1) 2, 11, 23,
2)
3)
12 and 24
4)
1 x 48 = 48
2 x 24 = 48
3x 16 = 48
5) 1 and 28,
2 and 14 ,
1, 2, 3, 4, 6, 8
4 x 12 = 48
6 x 8 = 48
4 and 7
6)1, 2, 5, 7, 10, 14, 35, 70
7) 14
8) 32 = 9 and 52 = 25; 9 x 25 = 225
9) x= 3 y = 7
10)
(a) 23 x 32 x 5
(b) 7
15 minutes for 15 days
…£40…….
R
E
Probability
D
15-4-15
1)
2) 0.92
4) 0.3x0.3=0.09
3)
5/9
5) 1-(0.15+0.3+0.3)=0.25
6)
Pythagoras
1. Hypotenuse
2) 16
4) Square both sides, add them, then find the square root
5.
42 + 52 = x2
16 + 25 = x2
41 = x2
X = 6.4 cm to 1 d.p.
6.
AB2 = 52 + 72
= 25 + 49
= 74
AB = 8.60 cm to 2.d.p
Ratio and proportion
1)
100  (2 + 3) x 2 = £40
2)
3)
(b) £4 200
(a) 21 000  (2+3+5) x 2 = £4 200
4) (a) 1 234  1.7 = £725.88
5)
150  (2 + 3) x 3 = £90
(b) 400 x 1.7 = 680 euros
(a) 900 x 2 = 1800ml
6) (a) 20  (4 + 1) x 4 = 16g
(b) (5) 55:45 (5)
11:9
(c)
(11)
3) 12
(b) 750  5 x 6 = 900ml
11: 9 (11)
1 : 0.82
15 minutes for 15 days
R
E
Solving equations
1. D
x=5
15-4-15
2. a =
5. p =
8. n =
b) k=
4. c = 3.5
7. m = 6
10. a) t = 15
21
4
2
-9
3. y = 5
6. t = -2
9. x = 4
c)x = 2.5
Substitution, trial and improvement
1) 7 x 3 -1 = 20
2) 5 x 3 = 15
3) b = 2 x 9 + 7, answer b = 25
4) 5x3 – 4x(-4) , 15 + 16 answer = 31
5) 3 x ( 3 – 8 ) = 3 x -5 , answer -15
6) 3 x 42 = 3 x 16, answer 48
7) 12 x 6 + 15, answer 87 minutes or 1 hour and 27 minutes NOT 1.27 hours! OR 1 hour 45
minutes (by dividing by 60)
8) n = 7
4.1
73.021
9) x = 4.6
4.2
78.288
4.3
83.807
4.4
89.584
4.5
95.625
4.55
98.74638
4.6
101.936
Speed, distance and time
1) (a) 2 hrs 15 mins
(b)1 hr 48 mins (.8x60)
2) (a) 0.5
(b) 1.75 (4560)
3) (a) 120 miles
(c) 3 hrs 33 mins (.55x60)
(c) 2.35 (2160)
(b) 15 miles
4) 2400  6 = 400 km per hour
5) 570  150 = 3.8 hours = 3 hours 48 minutes (0.8 x 60)
6)
200  1000 = 0.2 km
0.2  20
= 0.01 km per sec
0.01 x 60 (secs per min) x 60 (mins per hour) = 36 km per hour
Standard form,
1.
2.
3.
4.
5.
6.
7.
8.
indices and roots
9
5
47
72
106
f9
r-2
10y9
9.
10.
11.
12.
13.
14.
15.
2k5
10m6n7
3.5 x 10 9
5.43 x 10-7
12 900 000
1.5 x 10 11
a) 4.2 x 109 km
b) 3 400 000 kg
Transformations
The answers are easiest worked out while marking – or look on the master!
15 minutes for 15 days