Daily Practice · Higher Plus
July 2015 - Higher Plus 5-a-day
Every Higher Plus sheet published in July 2015, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' July 2015 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in July 2015
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st July 2015f(x) = 8x - 3. Work out the inverse function f^-1(x).
- 2nd July 2015y is directly proportional to x^3. When x = 3, y = 135. Work out y when x = 2.
- 3rd July 2015In a vector proof you find that vector PQ = 3a + 2b and vector RS = 12a + 8b. What does this show about PQ and RS?
- 4th July 2015A bag holds 6 red and n blue counters. The probability of taking a red is 6/13. Work out n.
- 5th July 2015A histogram has two bars: one 20 units wide with frequency density 2, one 25 units wide with density 3. How many values in total?
- 6th July 2015A block has mass 380 g (to the nearest 10 g) and volume 14 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 7th July 2015Solve x^2 + y^2 = 289 and y = x - 7 simultaneously.
- 8th July 2015y is directly proportional to sqrt(x). When x = 25, y = 10. Work out y when x = 9.
- 9th July 2015A cuboid measures 14 cm by 12 cm by 3 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 10th July 2015A bag holds 5 red and 6 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 11th July 2015On a histogram, a 5-wide bar and a 20-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 12th July 2015x = 177 and y = 10, each correct to the nearest whole number. Work out the upper bound of x - y.
- 13th July 2015Use the iteration x(n+1) = cube root of (3x(n) + 5) with x(0) = 5. Work out x(1) to 3 decimal places.
- 14th July 2015A train slows steadily from 26 m/s to rest in 8 seconds. Work out its deceleration.
- 15th July 2015A cuboid measures 14 cm by 5 cm by 8 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 16th July 2015A bag holds 7 red, 6 blue and 4 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 17th July 2015A histogram has two bars: one 10 units wide with frequency density 1.2, one 10 units wide with density 3. How many values in total?
- 18th July 2015A car covers 210 m (to the nearest 10 m) in 6 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 19th July 2015Work out the nth term of the quadratic sequence -1, 1, 5, 11, ...
- 20th July 2015y is inversely proportional to x^2. When x = 4, y = 36. Work out y when x = 3.
- 21st July 2015The point (3, 4) lies on the circle x^2 + y^2 = 25. Work out the gradient of the tangent to the circle at that point.
- 22nd July 2015A bag holds 10 counters, r of them red. Two are taken without replacement and P(both red) = 1/3. Work out r.
- 23rd July 2015On a histogram, a 10-wide bar and a 30-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 24th July 2015Rationalise the denominator of 84/sqrt(7), giving your answer in its simplest form.
- 25th July 2015The point (-1, -3) lies on y = f(x). Write down its image on y = f(-x).
- 26th July 2015y is directly proportional to x^3. When x = 3, y = 81. Work out y when x = 2.
- 27th July 2015In a circle theorem proof, a step uses the fact that the exterior angle of a cyclic quadrilateral is being found. State the reason being quoted.
- 28th July 2015The probability of winning a game is 3/5. A player expects 54 wins. How many games did they play?
- 29th July 2015A histogram has two bars: one 20 units wide with frequency density 1.5, one 25 units wide with density 0.6. How many values in total?
- 30th July 2015Simplify sqrt(18) + sqrt(18), giving your answer in the form a sqrt(b).
- 31st July 2015Prove that the sum of 3 consecutive integers is always a multiple of 3. State the simplified sum you would use.