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f(x)= 5 - x and g(x)= 3x + 7. Simplify f(2x) + g(x-1) (2018 past paper question)

If f(x)= 5 - x then f(2x)= 5 - 2x If g(x)= 3x + 7 then g(x-1)= 3(x-1) +7 = 3x - 3 + 7 = 3x +4
So f(2x) + g(x-1) = 5 - 2x + 3x + 4 = 9 + x

Answered by Jess B. • Maths tutor

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Grade 8/9 question: Point A (0,1) and Point B (10,6) lie on a straight line. Find the equation of the line perpendicular to AB which also intersects B.

Gradient of AB: Change in Y/ Change in X .... (6-1)/(10-0) = 0.5Gradient of line perpendicular to AB: NEGATIVE (flip the sign) RECIPROCAL (flip th...

Answered by Kim R. • Maths tutor

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The numbers a,b,c and d satisfy the equations: a+2b+3c+4d=k and 4a=3b=2c=d. What is the smallest value of k for which a,b,c and d are positive integers?

The key thing to notice here is that d must have the factors 4,3 and 2. The number 12 is the smallest to contain all those factors. We can then deduce c=6, b=4 and a=3 to get k=77.

Answered by Dean Y. • Maths tutor

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Find an expression for the nth term of this sequence: 3 - 11 - 19 - 27 - 35 . The nth term of a different sequence is 2n^3 + 3. Write down the first 3 terms of this sequence.

First, the sequence is 3 - 11 - 19 - 27 - 35. Looking at it, we can observe that each element of the sequence is created by adding 8 to the previous. The first term is 3. The second term is 3 + 8...

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The equation of a curve is y = x^2 + ax + b where a and b are integers. The points (0,-5) and (5,0) lie on the curve. Find the coordinates of the turning point of the curve.

In the equation for our line we have 2 unknowns: a and b. However, we know that the line passes through two known points with x and y coordinates. Therefore, we can begin by substituting in our known x an...

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