Algebraic Equations and Inequalities
Simplify the expression: 2x+5−3x
−x+5
What is the y-intercept of the graph y=2x+3?
3
What is the common difference in the arithmetic sequence: 3, 7, 11, 15...?
4
If you invest R1000 at an annual interest rate of 5% compounded annually, what will the amount be after 1 year?
R1050.
What is sin90∘?
1
Solve for x: 3x−7=5.
x=4.
Determine whether the function y=−x2+4x has a maximum or minimum value.
Maximum value (since the coefficient of x^2 is negative)
Find the 5th term in the geometric sequence where the first term is 2 and the common ratio is 3.
162 (using an=2×3^n−1)
Calculate the simple interest on an amount of R2000 invested at 6% per annum for 3 years.
R360.
Find the value of cos60∘
0.5
Solve the inequality: 2x+1>5.
x>2
If f(x)=2x+1 and g(x)=x2−4, find f(g(2)).
f(g(2))=f(0)=2×0+1=1.
What is the sum of the first 4 terms of the arithmetic sequence: 5, 8, 11, 14?
50
What is the formula for calculating compound interest?
A=P(1+100/r)n.
Simplify: sin2 θ+cos2 θ
1
Simplify: 3x2−6x\3x
x−2 (for x≠0).
Determine the roots of the function y=x2−9.
x=−3x and x=3.
Find the sum of the first 6 terms of the geometric sequence: 2, 4, 8, 16...
126
If R10,000 is invested at an annual interest rate of 8% compounded quarterly, find the value of the investment after 2 years.
Approximately R11,716.59.
Solve for θ in the equation tanθ=1 where 0∘≤θ≤180∘
θ=45∘ or θ=225∘
Solve for x in the equation: x2−5x+6=0
x=2 or x=3x
Given the function f(x)=3x−2, find the inverse function f−1(x).
f−1(x)=x+2/3.
If the sum of the first n terms of an arithmetic sequence is given by Sn=3n2−n, find the 4th term.
21 (using T4=S4−S3).
Calculate the present value of R5000 due in 3 years if the annual interest rate is 10% compounded annually.
Approximately R3,756.57.
If sinx=1/2 and 0∘≤x≤360∘ , find all possible values of x.
x=30∘ or x=150∘