ullswater community college · web viewmake x the subject of y=7x+1 . find the value of 3 1 4 - 2...

A Level Maths Summer Preparation Booklet.

Everything in this booklet is also in the higher GCSE Revision Guide. You must complete the work in this booklet before your first A Level lesson in September. Bring your work (done on paper) to the first lesson where it will be collected.

Section 1.a) Simplify 3 x×14 yb)Expand and simplify 3 ( x+4 )+2(x+1)

c) Expand and simplify (x+1)(x−1)d)Factorise 3 xy+6 x2

e)Make x the subject of y=3 x−7f) Find the value of 1 12 +3

5

g) Solve 3−x=5h)Solve ( x+3 ) ( x−2 )=0

i) Solve the simultaneous equations 3 x+ y=5 4 x− y=2

j) Simplify √2×√18

k) What is the gradient of the line 4 y−x=8l) Simplify 1x +

3x

m) Simplify m4×m−2

n)Find the value of x

4

3x

o)Write down the quadratic formula.

Section 2.a) Simplify 0.5 x2−2 x2

b)Expand and simplify 5 ( x−1 )+3(2 x+4)

c) Expand and simplify (x+4 )2

d)Factorise 4 p−8 pqe)Make x the subject of y=x2

f) Find the value of 34 ÷7

g) Solve 1−3w=15+4w

h)Solve x2−2 x−3=0i) Solve the simultaneous equations 4 x+5 y=19

−4 x+3 y=5

j) Simplify √20k) Write down the equation of the line with gradient

3 that goes through the point (0,5 )

l) Simplify xy ×3x

m) Simplify e7÷e4

8

6

x


o)Write down the cosine rule.

Section 3.a) Simplify 4 pq−2 p×3qb)Expand and simplify 12 (4 x−3 )+1

2(6 x+3)

c) Expand and simplify (x−6)(x+6)d)Factorise 10+5 ye)Make x the subject of y=4−xf) Find the value of 1 45×1

12

g) Solve 2 x−7=2+ xh)Solve x2−2 x=3i) Solve the simultaneous equations 6 x+ y=7

4 x+ y=5

j) Rationalise 3√2k) Find the y intercept of 3 x= y−7l) Simplify mn + n

m

m) Simplify (h6)2


o)Sketch the graph of y=x2.

Section 4.a) Simplify 3 xy×4 yb)Expand and simplify 7 (3 x−4 )+2(4−x)

c) Expand and simplify x (x+3)( x−1)d)Factorise x2+3x+4e)Make x the subject of y=7 x+1f) Find the value of 3 14−

211

g) Solve 3x +1=2

h)Solve x2+8 x+15=0i) Solve the simultaneous equations 8 x+3 y=8

5 x−3 y=5

j) Expand and simplify √3(1−√3)

x116

k) Write down the equation of a line parallel to y=7 x−3

l) Simplify 3x−1x2

m) Simplify 3a4b×2b2


o)Write down the sine rule.

Section 5.a) Simplify 5m2×3mb)Expand and simplify 3 (10−x )−3(x+10)

c) Expand and simplify (3 x−1)(2 x+2)d)Factorise 6 p2q+9 pq4

e)Make x the subject of y= x3−10

f) Simplify 3× 25 y

g) Solve 3 ( x−1 )=9

h)Solve x2+ x−12=0i) Solve the simultaneous equations 6 x+2 y=5

2 x+2 y=3

61.7

x

j) Simplify √5×√20

k) Write down the equation of a line perpendicular to y=7 x−3

l) Find the value of 7 12×35

m) Simplify m6

m4


o)Sketch the sine graph between 0o and 360o

Section 6.a) Simplify (2 gh)2

b)Expand and simplify 5 (2x+1 )−4 (x−3)

c) Expand and simplify 5(x+3)(x−1)d)Factorise x2−x−6e)Make x the subject of y=1xf) Simplify 2x +

1x

g) Solve 8 (2 x+1 )=3(5 x+3)

h)Solve (2 x−1)( x+1)=0

x

130o

i) Solve the simultaneous equations 2 x+ y=8 3 x−2 y=5

j) Simplify √54k) Write down the equation of the line which goes

through (1,4) and (4 ,−2)l) Simplify 5x +

1y

m) Simplify 12a2b6

3 a6b5


o)Solve 4 x2+7 x−9=0

Section 7.a) Simplify 14 pq2÷3.5 pqb)Expand and simplify 3 x (4 x−7 )−2(6−x)

c) Expand and simplify (4 x+1)(x−6)d)Factorise 5m3n+15m2n3

e)Make x the subject of y=1x +2

f) Simplify 89 ÷xy

x

√5

3

g) Solve x+13 =2+x

h)Solve x2+9 x=10i) Solve the simultaneous equations 4 x+ y=21

3 x−3 y=12

j) Rationalise 7√3k) What is the gradient of the line 3 x+7 y=14l) Simplify a4− b

12

m) Simplify (5 g f 2)3


o)In a test the boys mean score was 17.5 and their range was 15. The girls had a mean score of 21.3 and their range as 26. Interpret what these statistics mean.

Section 8.a) Simplify 5u2×3u2

b)Expand and simplify 11 ( x−1 )−3 (x−4 )

c) Expand and simplify (2 x−3)(3 x+2)d)Factorise x2−8 x+12e)Make x the subject of y=5 x+3x

x6

4

f) Simplify 1x−12

g) Solve 4+2 x=−8

h)Solve x2+10x=0i) Solve the simultaneous equations 2 x− y=6

4 x+3 y=22

j) Simplify (3√5)2

k) What is the equation of the line which passes through (1,4) and (4 ,−2)

l) Simplify x6 ÷2x

m) Simplify (m3n2)6


o)Sketch the cosine graph between 0o and 360o.

Section 9.a) Simplify 3 x+11 y−(−x)

b)Expand and simplify 14 (3 x+16 )+ 34(4 x+1)

c) Expand and simplify (x−4)(x+4)

x125

d)Factorise 2 x2+3 x+1e)Make x the subject of y=4 x2−3f) Simplify 2x ×

1x

g) Solve 4 ( x+1+3 x )=4 x+22

h)Solve x2−9=0 (find both answers)i) Solve the simultaneous equations y=x+8

x+ y=14

j) Simplify √108k) What is the equation of the y axis?l) Calculate 7÷1 12m) Simplify 4m3n×7mn6

n)Is this triangle right angled?

o)Sketch the graph of y=x3.

Section 10.a) Simplify x2−(3 x+4 x2)

8.21

4

7

b)Expand and simplify −3 (4 x+1 )+3(1−4 x)

c) Expand and simplify (3−x)(x−3)d)Factorise 6 s t2−12t 3+24 ste)Make x the subject of y= 1

x+1

f) Simplify x2

4÷ x2

g) Solve x+42 =34

h)Solve x2−144=0i) Solve the simultaneous equations y=2x+4

y=x+7

j) Simplify 5(2+√7)2

k) What is the equation of the x axis?l) Simplify 3a7 ×

14a

m) Simplify 3m2×2mn

(2nm1.5)2


o)A fair coin is tossed three times. What is the probability of it landed on tails three times in a row?

Section 11.

x

12

6

a) Simplify 6 rs×3 t ÷4 sb)Expand and simplify 5 (2x−11)−3 (2x−1)

c) Expand and simplify (2 x+7)2

d)Factorise x2+ x−20e)Make x the subject of y=8x3

f) Evaluate 17×1013

g) Solve 15 (10 x+1 )=12(8 x−10)

h)Solve 2 x2+3 x+1=0i) Solve the simultaneous equations 3 x+2 y=8

5 x+3 y=13

j) Simplify 2√72k) Write down he equation of the line which goes

through (1,1) and has a gradient of 0.5l) Simplify 32x−

13 y

m) Simplify (√3 x4)3


o)Write down at least three formulae which involve speed, distance and time.

5

x25o

Section 12.a) Simplify 2 j2×4 j−3 k5

b)Expand and simplify 7 ( x−8 )+4 (2x−5)

c) Expand and simplify (x+6)( y−x )(x+3)d)Factorise x2+7x+6e)Make x the subject of y= 1

5√ x

f) Simplify 14 x3 + 2x5

g) Solve 10−x=3 x−6h)Solve 2 x2−10x−12=0i) Solve the simultaneous equations 4 x+2 y=10

7 x+3 y=16

j) Rationalise 1√8k) What is the gradient of 4 y=x+13l) Simplify 2

x+1× 1x−1

m) Simplify (3.9×1014)÷ (1.3×1012)


o)Sketch the tan graph between 0o and 360o.

12

8

x

Section 13.a) Simplify √9 x2

b)Expand and simplify 18 (2−x )−16 (3 x+1)

c) Expand and simplify (3 p+4 )2(5−p)d)Factorise 3m2n+6mn2+m2n2

e)Make x the subject of y= x+32f) Evaluate 14÷ x 14g) Solve 3 x−1.5=4 (x+0.5)h)Solve 3 x2−12=0i) Solve the simultaneous equations 2 x+9 y=1

5 x−4 y=29

j) Simplify (√2+3)(3−√2)

k) What is the equation of the line parallel to y=5−2 x which goes through the point (0,0)

l) Simplify 2ef −1f 2

m) Simplify 10e2 f 3

2ef ×7e2

n)Find the value of x x6.1

5.3

o)Sketch the graph of y=1x

Section 14.a) Simplify (√2x )4

b)Expand and simplify 5 (x2+1 )+3x (x−2)

c) Expand and simplify (x2+1)(x−2)d)Factorise 4 x2−36e)Make x the subject of y= x+3

−x+1

f) Simplify 3 x× 16g) Solve x2 + 3x

4=15

h)Solve x2+9 x+20=0i) Solve the simultaneous equations 3x−8 y=5

5 x−12 y=9

j) Rationalise √3√6k) Write down the equation of the line which goes

through (2,15) and has a gradient of 7.l) Simplify 1x ÷4.5

m) Simplify √8a2b5×√2a3b

n)Find the value of x 30o

√12

x

o)Expand and simplify (x+3)3

Section 15.a) Simplify 21 t−t2+3 t−(−2 t )3+t

b)Expand and simplify 4 x2 (3−x )+x2(2+x)

c) Expand and simplify (3 x−4 y)(x+2)d)Factorise x2−144e)Make x the subject of y=x2+3 xf) Simplify 12x +

38 x2

g) Solve 3 ( x−1 )=5 (x+1)

h)Solve 3 x2−x−2=0 i) Solve the simultaneous equations x+2=6 y

8 y−1=3 x

j) Rationalise 4√5k) What is the gradient of 3 x−4 y=1l) Simplify x3 ×

2x−2

m) Simplify 12m4n3

n)Is this triangle right angled? 6.10

3.17

5.21

o)What is the value of 3+1×42

ullswater community college · web viewmake x the subject of y=7x+1 . find the value of 3 1 4 - 2...

Documents