Daily Practice · Higher Plus
February 2013 - Higher Plus 5-a-day
Every Higher Plus sheet published in February 2013, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' February 2013 sheets in a single PDF, each tier behind its own divider page - 140 sheets in one file.
Every sheet in February 2013
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st February 2013The point (10, 24) lies on the circle x^2 + y^2 = 676. Work out the gradient of the tangent to the circle at that point.
- 2nd February 2013A bag holds 12 counters, r of them red. Two are taken without replacement and P(both red) = 1/66. Work out r.
- 3rd February 2013On a histogram, a 10-wide bar and a 30-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 4th February 2013A block has mass 720 g (to the nearest 10 g) and volume 25 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 5th February 2013The curve y = cos x° is drawn for 0 <= x <= 360. Write down the value of y when x = 90.
- 6th February 2013A train slows steadily from 26 m/s to rest in 4 seconds. Work out its deceleration.
- 7th February 2013In a circle theorem proof, a step uses the fact that opposite angles of a cyclic quadrilateral are being proved. State the reason being quoted.
- 8th February 2013The probability of winning a game is 1/4. A player expects 7 wins. How many games did they play?
- 9th February 2013A histogram has two bars: one 20 units wide with frequency density 2.5, one 20 units wide with density 3.5. How many values in total?
- 10th February 2013x = 103 and y = 19, each correct to the nearest whole number. Work out the upper bound of x - y.
- 11th February 2013A quadratic sequence starts 9, 21, 41, 69. Work out the second difference, and the coefficient of n^2.
- 12th February 2013y is inversely proportional to x^2. When x = 4, y = 12. Work out y when x = 2.
- 13th February 2013In a vector proof you find that vector PQ = 2a + 6b and vector RS = 8a + 24b. What does this show about PQ and RS?
- 14th February 2013A bag holds 8 red and n blue counters. The probability of taking a red is 8/13. Work out n.
- 15th February 2013On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 16th February 2013A car covers 220 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.
- 17th February 2013Solve x^2 - 3x > 0.
- 18th February 2013y is directly proportional to x^3. When x = 3, y = 54. Work out y when x = 5.
- 19th February 2013A cuboid measures 9 cm by 12 cm by 15 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 20th February 2013A bag holds 4 red and 4 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 21st February 2013A histogram has two bars: one 20 units wide with frequency density 2.5, one 20 units wide with density 1.4. How many values in total?
- 22nd February 2013Rationalise the denominator of 20/sqrt(2), giving your answer in its simplest form.
- 23rd February 2013Write x^2 + 16x - 6 in the form (x + a)^2 + b.
- 24th February 2013y is directly proportional to sqrt(x). When x = 25, y = 35. Work out y when x = 16.
- 25th February 2013A cuboid measures 7 cm by 5 cm by 4 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 26th February 2013A bag holds 4 red, 5 blue and 6 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 27th February 2013On a histogram, a 4-wide bar and a 8-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 28th February 2013Simplify sqrt(45) + sqrt(180), giving your answer in the form a sqrt(b).