Grade 9
Solve for x:3x+5=17
Answer: x=4
Find all real roots of the quadratic equation: x^2−9=0
Answer: x=3 and x=−3
State the domain and range of the rational function f(x)=x−51
Answer: Domain={XeR}
Range={YeR}
Find the derivative of the polynomial function f(x)=4x3−5x2+7.
Answer: f′(x)=12x^2−10x
Find the slope of the line passing through the points (2,3) and (6,11).
m=2
In a right-angled triangle, one leg measures 6 cm and the hypotenuse measures 10 cm. What is the length of the other leg?
Answer: 8 cm
Solve the trigonometric equation sin(x)=0.5 for the interval from 0∘ to 360∘
Answer: x=30∘ and x=150∘
Evaluate the limit: limx→3 (x^2−9)/x−3
Answer: 6
Factor the expression: x^2−2x−15
Answer:(x+3)(x−5)
Convert the quadratic equation y=x^2−6x+8 into vertex form by completing the square.
Answer: y=(x−3)^2−1
Find the maximum or minimum value of the parabola given by f(x)=−2x^2+8x−3.
Answer: Maximum value is 5
Find the inverse function f−1(x) for the linear function f(x)=2x+5.
Answer: f−1(x)=(x−5)/2
The interior angles of a triangle are in the ratio 2:3:4. What is the measure of the largest angle?
Answer:80∘
Find the y-intercept of the quadratic function given in factored form: y=−2(x−3)(x+4)
Answer: 24
In an arithmetic sequence, the 3rd term is 11 and the 7th term is 27. What is the 10th term?
Answer: 39
Find the absolute maximum value of the function f(x)=x^3−3x^2 on the closed interval [0,4].
Answer: 16
If $500 is invested at a simple interest rate of 4% per year, how many years will it take to earn $100 in total interest?
Answer: 5 years
A circle has its center at the origin (0,0) and passes through the point (3,4). What is the radius of the circle?
Answer: r=5
Evaluate the logarithmic expression without a calculator: log2(32)+log3(81)−log5(125)
Answer: 6
Evaluate the indefinite integral: ∫(6x^2−4x+3)dx
Answer: 2x^3−2x^2+3x+C