Daily Practice · Higher Plus
March 2012 - Higher Plus 5-a-day
Every Higher Plus sheet published in March 2012, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' March 2012 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in March 2012
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st March 2012y is directly proportional to sqrt(x). When x = 49, y = 42. Work out y when x = 16.
- 2nd March 2012A cuboid measures 7 cm by 5 cm by 8 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 3rd March 2012A bag holds 5 red, 7 blue and 4 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 4th March 2012On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 5th March 2012A block has mass 270 g (to the nearest 10 g) and volume 10 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 6th March 2012Use the iteration x(n+1) = cube root of (11x(n) + 3) with x(0) = 1. Work out x(1) to 3 decimal places.
- 7th March 2012A train slows steadily from 33 m/s to rest in 8 seconds. Work out its deceleration.
- 8th March 2012The point (7, 24) lies on the circle x^2 + y^2 = 625. Work out the gradient of the tangent to the circle at that point.
- 9th March 2012A bag holds 6 counters, r of them red. Two are taken without replacement and P(both red) = 1/5. Work out r.
- 10th March 2012A histogram has two bars: one 20 units wide with frequency density 0.4, one 10 units wide with density 1.4. How many values in total?
- 11th March 2012x = 130 and y = 100, each correct to the nearest whole number. Work out the upper bound of x - y.
- 12th March 2012Work out the nth term of the quadratic sequence 8, 16, 28, 44, ...
- 13th March 2012y is inversely proportional to x^2. When x = 4, y = 25. Work out y when x = 5.
- 14th March 2012In a circle theorem proof, a step uses the fact that a tangent meets a radius at the point of contact. State the reason being quoted.
- 15th March 2012The probability of winning a game is 3/4. A player expects 27 wins. How many games did they play?
- 16th March 2012On a histogram, a 4-wide bar and a 12-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 17th March 2012A car covers 400 m (to the nearest 10 m) in 5 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 18th March 2012The point (6, 6) lies on y = f(x). Write down its image on y = f(x - 1).
- 19th March 2012y is directly proportional to x^3. When x = 4, y = 256. Work out y when x = 3.
- 20th March 2012In a vector proof you find that vector PQ = 2a + 6b and vector RS = 8a + 24b. What does this show about PQ and RS?
- 21st March 2012A bag holds 2 red and n blue counters. The probability of taking a red is 1/3. Work out n.
- 22nd March 2012A histogram has two bars: one 20 units wide with frequency density 2, one 10 units wide with density 0.6. How many values in total?
- 23rd March 2012Rationalise the denominator of 60/sqrt(6), giving your answer in its simplest form.
- 24th March 2012Prove that the sum of 9 consecutive integers is always a multiple of 9. State the simplified sum you would use.
- 25th March 2012y is directly proportional to sqrt(x). When x = 4, y = 4. Work out y when x = 36.
- 26th March 2012A cuboid measures 13 cm by 11 cm by 15 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 27th March 2012A bag holds 5 red and 4 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 28th March 2012On a histogram, a 5-wide bar and a 20-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 29th March 2012Simplify sqrt(27) + sqrt(12), giving your answer in the form a sqrt(b).
- 30th March 2012f(x) = 4x - 2 and g(x) = 3x - 7. Work out fg(4).
- 31st March 2012A train slows steadily from 20 m/s to rest in 10 seconds. Work out its deceleration.