Daily Practice · Higher Plus
February 2012 - Higher Plus 5-a-day
Every Higher Plus sheet published in February 2012, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' February 2012 sheets in a single PDF, each tier behind its own divider page - 145 sheets in one file.
Every sheet in February 2012
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st February 2012A cuboid measures 4 cm by 5 cm by 8 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 2nd February 2012A bag holds 4 red, 4 blue and 4 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 3rd February 2012A histogram has two bars: one 5 units wide with frequency density 1.2, one 5 units wide with density 3. How many values in total?
- 4th February 2012A car covers 870 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.
- 5th February 2012Make x the subject of 5x + 3 = y(x + 3).
- 6th February 2012y is directly proportional to sqrt(x). When x = 25, y = 10. Work out y when x = 4.
- 7th February 2012The point (9, 12) lies on the circle x^2 + y^2 = 225. Work out the gradient of the tangent to the circle at that point.
- 8th February 2012A bag holds 6 counters, r of them red. Two are taken without replacement and P(both red) = 1/15. Work out r.
- 9th February 2012On a histogram, a 10-wide bar and a 20-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 10th February 2012Rationalise the denominator of 45/sqrt(5), giving your answer in its simplest form.
- 11th February 2012Write 5/(x + 6) + 7/(x + 1) as a single fraction.
- 12th February 2012A train slows steadily from 15 m/s to rest in 4 seconds. Work out its deceleration.
- 13th February 2012In a circle theorem proof, a step uses the fact that the three angles of triangle OAB are being summed. State the reason being quoted.
- 14th February 2012The probability of winning a game is 9/10. A player expects 126 wins. How many games did they play?
- 15th February 2012A histogram has two bars: one 10 units wide with frequency density 1.2, one 10 units wide with density 3.5. How many values in total?
- 16th February 2012Simplify sqrt(18) + sqrt(32), giving your answer in the form a sqrt(b).
- 17th February 2012Solve 2x^2 - 11x + 12 = 0.
- 18th February 2012y is inversely proportional to x^2. When x = 3, y = 100. Work out y when x = 5.
- 19th February 2012In a vector proof you find that vector PQ = 2a - 6b and vector RS = 6a - 18b. What does this show about PQ and RS?
- 20th February 2012A bag holds 2 red and n blue counters. The probability of taking a red is 2/9. Work out n.
- 21st February 2012On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 22nd February 2012A rectangle is 10 cm by 22 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 23rd February 2012f(x) = 7x - 3. Work out the inverse function f^-1(x).
- 24th February 2012y is directly proportional to x^3. When x = 2, y = 16. Work out y when x = 3.
- 25th February 2012A cuboid measures 7 cm by 3 cm by 13 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 26th February 2012A bag holds 3 red and 8 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 27th February 2012A histogram has two bars: one 5 units wide with frequency density 1.2, one 10 units wide with density 0.8. How many values in total?
- 28th February 2012Expand and simplify (9 + sqrt(10))(9 - sqrt(10)).
- 29th February 2012Solve x^2 + y^2 = 25 and y = x + 1 simultaneously.