Daily Practice · Higher Plus
February 2014 - Higher Plus 5-a-day
Every Higher Plus sheet published in February 2014, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' February 2014 sheets in a single PDF, each tier behind its own divider page - 140 sheets in one file.
Every sheet in February 2014
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st February 2014A train slows steadily from 31 m/s to rest in 5 seconds. Work out its deceleration.
- 2nd February 2014In 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.
- 3rd February 2014The probability of winning a game is 1/5. A player expects 14 wins. How many games did they play?
- 4th February 2014A histogram has two bars: one 10 units wide with frequency density 2, one 10 units wide with density 0.8. How many values in total?
- 5th February 2014A rectangle is 14 cm by 10 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 6th February 2014f(x) = 5x + 11. Work out the inverse function f^-1(x).
- 7th February 2014y is inversely proportional to x^2. When x = 3, y = 108. Work out y when x = 6.
- 8th February 2014In a vector proof you find that vector PQ = 4a + 4b and vector RS = 8a + 8b. What does this show about PQ and RS?
- 9th February 2014A bag holds 4 red and n blue counters. The probability of taking a red is 1/2. Work out n.
- 10th February 2014On a histogram, a 5-wide bar and a 10-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 11th February 2014Expand and simplify (8 + sqrt(3))(8 - sqrt(3)).
- 12th February 2014Solve x^2 + y^2 = 841 and y = x - 1 simultaneously.
- 13th February 2014y is directly proportional to x^3. When x = 3, y = 54. Work out y when x = 4.
- 14th February 2014A cuboid measures 14 cm by 12 cm by 5 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 15th February 2014A bag holds 6 red and 3 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 16th February 2014A histogram has two bars: one 10 units wide with frequency density 1.5, one 5 units wide with density 0.6. How many values in total?
- 17th February 2014A block has mass 630 g (to the nearest 10 g) and volume 17 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 18th February 2014Use the iteration x(n+1) = cube root of (8x(n) + 2) with x(0) = 3. Work out x(1) to 3 decimal places.
- 19th February 2014y is directly proportional to sqrt(x). When x = 49, y = 56. Work out y when x = 81.
- 20th February 2014A cuboid measures 14 cm by 4 cm by 10 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 21st February 2014A bag holds 7 red, 6 blue and 5 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 22nd February 2014On a histogram, a 4-wide bar and a 16-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 23rd February 2014x = 99 and y = 46, each correct to the nearest whole number. Work out the upper bound of x - y.
- 24th February 2014Work out the nth term of the quadratic sequence -9, -8, -3, 6, ...
- 25th February 2014A train slows steadily from 24 m/s to rest in 5 seconds. Work out its deceleration.
- 26th February 2014The point (8, 15) lies on the circle x^2 + y^2 = 289. Work out the gradient of the tangent to the circle at that point.
- 27th February 2014A bag holds 9 counters, r of them red. Two are taken without replacement and P(both red) = 1/12. Work out r.
- 28th February 2014A histogram has two bars: one 10 units wide with frequency density 0.4, one 20 units wide with density 3. How many values in total?