Solve the pairs of simultaneous equations.
2x2+xy+1=0
x+y=2
Give your answer as x=?,y=?
x=-1,y=3
100
Simplify 4√ 2-√ 8+√ 50
7√ 2
100
Find the value of the polynomial P(x)=3x2-7x+2 at x=4
22
100
What is the amplitude of y=2 sin 3x+3?
2
100
If M(3,5) is the midpoint of the line joining A(-3,7) and B(p,q), find the value of p and q.
Give your answers as p=?,q=?
p=9,q=3
200
Solve the simultaneous equations:
2x+3y=7
3x-4y=2
Give your answer as y=?,x=?
y=1,x=2
200
Simplify (3√3 -3√2)(3√9+3√6+3√4)
1
200
Without expanding, find the coefficient of xx in (2x2-x+1)(3x-2) .
-7
200
What is 1+tan2x?
sec2x
200
If A(2,0), B(p,-2), C(-1,1) and D(3,r) are the vertices of a parallelogram ABCD, calculate the value of p and of r.
Give your answer as p=?,r=?
p=-2,r=3
300
The equation 2x2-x-2=0 has roots A and B. Find the value of A/B+B/A.
-9/4
300
Solve 3x^2=9x+1/27x
x=-2 or 1
300
Find the values of the unknown constants for x3+cx2+x+6=(x+1)(x-2)(ax+b)
State your answer as a=?,b=?,c=?
a=1,b=-3,c=-4
300
What is sin (90-A)?
cos A
300
Find the equation of the line with y-intercept 3 and parallel to the line y=3x+4
y=3x+3
400
The equation x2-3x-2=0 has roots A and B, and the equation x2-6x+q=0 has roots k/A and k/B. Find the value of k and q.
Give your answer as k=?,q=?
k=-4,q=-8
400
Solve the simultaneous equations
64(4y)=16x
3y=4(3x-2)-1
Give your answers as x=?,y=?. Note: there may be more than one pair of solutions
x=1,y=-1 or x=2,y=1
400
The polynomial 2x2+6x+3 has the same remainder when divided by x+p or by x-2q. Find the value of p-2q, where p is not equal to 2q.
3
400
Given that tan A=3/4, cos B=-3/5 and that A and B are in the same quadrant, evaluate tan B/cos A.
-5/3
400
Three points have coordinates A(2,6), B(6,-2) and C(3,-1). Find the coordinates of the foot of the perpendicular from C to AB.
(5,0)
500
Find the range of values of k for which 3x2-3x>x+k for all real values of x.
k<-4/3
500
Find x for which 27 x 3lg x=91+lg(x-20)
40
500
The remainder when 2x3+9x2+7x+3 is divided by x-k is 9. Find k. Note: there may be more than one answer.
Give your answer in ascending order.
-3,-2,1/2
500
Find all angles between 0 degrees and 360 degrees which satisfy cos (x+40)= 2 sin (x-10)
23.1, 203.1
500
The coordinates of A(3,5), B(-1-3) and C form a right-angled triangle ABC, where angle A=90 degrees. Given that the gradient of BC is 1/2 and that D is the foot of the perpendicular from A to BC, find the length of the perpendicular AD.