Maths NBT Skills Preparation for Matrics in South Africa

Identify the domain for the expression (2 − √(2 − x)) / (2x − 2) to be real by enforcing 2 − x ≥ 0 and 2x − 2 ≠ 0, i.e., x ≤ 2 and x ≠ 1.

Identify domain restrictions for a trig function by examining zeros at 0 and 180 degrees and asymptotes at 90-degree intervals, concluding x = 90k for integers k.

Learn how to calculate standard deviation by hand using the variance formula, compute the mean, deviations, squares, and the final square-root step for a four-term data set.

Rewrite the expression and form a common denominator, apply the difference of squares to factor, cancel common factors, and obtain 1/(t+1).

This lecture analyzes solving (2x+1)/(x-1) ≤ 1, showing how assuming x>1 leads to a contradiction and concluding no solution, emphasizing careful checking to avoid assumptions.

Compare the given options, apply double-angle identities to rewrite expressions as cos 2x and 2 cos^2 x − 1, and identify the correct choice by factoring.

Learn to solve nested radical problems by squaring both sides and using an infinite sequence of square roots to deduce a from 64 minus a equals eight.

The lecture demonstrates using the remainder factor theorem to determine what to add to a polynomial so it becomes a factor, by descending powers and substituting k to obtain zero.

Solve quadratics by applying the quadratic formula to x^2 - x - 1 = 0, yielding x = (1 ± sqrt(5))/2. Sum the roots to get 1.

Apply the derivative, substitute fractions such as one over eight and one over sixty four, and apply the inverse by swapping x and y to reach the final result.

Multiply the counts of each letter in the word victory, using 1×2×3×4×3×2×1 to obtain 144 and identify option a as correct.

Apply exponent rules to rewrite and combine bases, convert thousand to ten cubed, and simplify by canceling like terms to identify the correct option.

The lecturer demonstrates using the difference of squares to multiply 2188 and 2186 by computing (2188-2186) and (2188+2186), yielding 2 and 4374 respectively.

Determine where the gradient times the regional graph is negative: positive gradient below the x axis or negative gradient above, including the between a and negative eight cases.

Rewrite y = 8 - 10 sin x cos x as y = -5 sin 2x + 8 using the double-angle identity, then identify the maximum value as 13.

determine the axis of symmetry and turning point for y = -x^2 - 2x + k by substituting x = -2 to find a and k.

Simplify the expression t(x) = x^3/(2x) - 4x/(2x) to obtain t(x) = (1/2)x^2 - 2, highlighting its quadratic form and selecting the correct option.

Investigate whether a transformed sequence derived from a geometric progression forms an arithmetic progression by comparing differences and applying logarithm rules, concluding it is arithmetic.

Solve inequalities involving x-2 squared and x+1, identify zeros at x=2 and x=-1, and determine where the expression is less than zero.

Use the conjugate to remove the denominator: multiply 4/(√11−√7) by (√11+√7)/(√11+√7). The denominator becomes 4, the numerator simplifies to 4(√11+√7), yielding √11+√7 (option B).

Calculate the remaining pool after removing one tenth and then five percent, simplify to 9/10 x minus 5% of 9/10 x, and find that 85.5% of x remains.

Analyze the inequality f(x) = (x-5)^2 < -3 and show there is no solution since a square is always nonnegative.

Use the double-angle identity cos(2x)=1-2 sin^2 x to solve for sin^2 15°, substituting cos 30°=sqrt(3)/2 and isolating sin^2 15° to obtain the result.

Explore solving exponential equations from question 107, showing 5^x-1 = 0 gives x=0 while 2^x+4 = 0 has no solution because 2^x is never negative; thus x=0.

Factor out x to rewrite the equation as 3^x minus one plus thirty three x squared equals zero. Exponential and parabola graphs intersect at zero, giving x=0.

Apply Pythagoras to a rectangle with a 50 unit perimeter, relate the diagonal r to width w, and minimize r by setting its derivative to zero.

Determine how many ways four rugby nations can occupy the top three positions, given equal chances to win. Compute 4 × 3 × 2, yielding 24.

Substitute two points on the graph of 4x = a sin x + b to compute a and b, use sine values and quadrants, and solve the resulting simultaneous equations.