Daily Practice · Higher Plus
February 2016 - Higher Plus 5-a-day
Every Higher Plus sheet published in February 2016, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' February 2016 sheets in a single PDF, each tier behind its own divider page - 145 sheets in one file.
Every sheet in February 2016
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st February 2016A block has mass 340 g (to the nearest 10 g) and volume 12 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 2nd February 2016Use the iteration x(n+1) = cube root of (3x(n) + 6) with x(0) = 2. Work out x(1) to 3 decimal places.
- 3rd February 2016y is directly proportional to x^3. When x = 3, y = 162. Work out y when x = 2.
- 4th February 2016A cuboid measures 5 cm by 15 cm by 6 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 5th February 2016A bag holds 7 red and 5 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 6th February 2016A histogram has two bars: one 5 units wide with frequency density 0.4, one 25 units wide with density 0.6. How many values in total?
- 7th February 2016x = 89 and y = 42, each correct to the nearest whole number. Work out the upper bound of x - y.
- 8th February 2016Work out the nth term of the quadratic sequence 2, 4, 8, 14, ...
- 9th February 2016y is directly proportional to sqrt(x). When x = 16, y = 24. Work out y when x = 9.
- 10th February 2016A cuboid measures 10 cm by 4 cm by 12 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 11th February 2016A bag holds 3 red, 4 blue and 3 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 12th February 2016On a histogram, a 10-wide bar and a 20-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 13th February 2016A car covers 170 m (to the nearest 10 m) in 2 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 14th February 2016The point (6, -6) lies on y = f(x). Write down its image on y = f(x - 3).
- 15th February 2016A train slows steadily from 16 m/s to rest in 5 seconds. Work out its deceleration.
- 16th February 2016The point (9, 40) lies on the circle x^2 + y^2 = 1681. Work out the gradient of the tangent to the circle at that point.
- 17th February 2016A bag holds 8 counters, r of them red. Two are taken without replacement and P(both red) = 3/14. Work out r.
- 18th February 2016A histogram has two bars: one 10 units wide with frequency density 0.4, one 20 units wide with density 3.5. How many values in total?
- 19th February 2016Rationalise the denominator of 24/sqrt(3), giving your answer in its simplest form.
- 20th February 2016Prove that the sum of 5 consecutive integers is always a multiple of 5. State the simplified sum you would use.
- 21st February 2016y is inversely proportional to x^2. When x = 5, y = 72. Work out y when x = 6.
- 22nd February 2016In a circle theorem proof, a step uses the fact that opposite angles of a cyclic quadrilateral are being proved. State the reason being quoted.
- 23rd February 2016The probability of winning a game is 7/8. A player expects 14 wins. How many games did they play?
- 24th February 2016On a histogram, a 10-wide bar and a 20-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 25th February 2016Simplify sqrt(12) + sqrt(147), giving your answer in the form a sqrt(b).
- 26th February 2016f(x) = 5x + 9 and g(x) = 2x + 2. Work out fg(2).
- 27th February 2016y is directly proportional to x^3. When x = 2, y = 16. Work out y when x = 3.
- 28th February 2016In a vector proof you find that vector PQ = a + 5b and vector RS = 3a + 15b. What does this show about PQ and RS?
- 29th February 2016A bag holds 4 red and n blue counters. The probability of taking a red is 2/3. Work out n.