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