Daily Practice · Higher Plus
February 2015 - Higher Plus 5-a-day
Every Higher Plus sheet published in February 2015, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' February 2015 sheets in a single PDF, each tier behind its own divider page - 140 sheets in one file.
Every sheet in February 2015
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st February 2015Solve x^2 + 8x + 7 < 0.
- 2nd February 2015y is inversely proportional to x^2. When x = 5, y = 72. Work out y when x = 6.
- 3rd February 2015In a vector proof you find that vector PQ = 2a + 5b and vector RS = 4a + 10b. What does this show about PQ and RS?
- 4th February 2015A bag holds 6 red and n blue counters. The probability of taking a red is 3/5. Work out n.
- 5th February 2015On a histogram, a 4-wide bar and a 16-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 6th February 2015Rationalise the denominator of 88/sqrt(11), giving your answer in its simplest form.
- 7th February 2015Write x^2 + 14x + 4 in the form (x + a)^2 + b.
- 8th February 2015y is directly proportional to x^3. When x = 3, y = 162. Work out y when x = 5.
- 9th February 2015A cuboid measures 15 cm by 3 cm by 4 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 10th February 2015A bag holds 10 red and 4 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 11th February 2015A histogram has two bars: one 20 units wide with frequency density 1.5, one 25 units wide with density 3. How many values in total?
- 12th February 2015Simplify sqrt(12) + sqrt(48), giving your answer in the form a sqrt(b).
- 13th February 2015Work out the coordinates of the turning point of y = x^2 + 2x - 15.
- 14th February 2015y is directly proportional to sqrt(x). When x = 49, y = 14. Work out y when x = 64.
- 15th February 2015A cuboid measures 5 cm by 8 cm by 12 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 16th February 2015A bag holds 6 red, 6 blue and 3 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 17th February 2015On a histogram, a 5-wide bar and a 10-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 18th February 2015A rectangle is 4 cm by 17 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 19th February 2015Simplify (x^2 + 2x - 35)/(x + 7).
- 20th February 2015A train slows steadily from 37 m/s to rest in 10 seconds. Work out its deceleration.
- 21st February 2015The 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.
- 22nd February 2015A bag holds 11 counters, r of them red. Two are taken without replacement and P(both red) = 2/11. Work out r.
- 23rd February 2015A histogram has two bars: one 10 units wide with frequency density 0.4, one 20 units wide with density 1.4. How many values in total?
- 24th February 2015Expand and simplify (2 + sqrt(2))(2 - sqrt(2)).
- 25th February 2015In an algebraic proof, how would you write the number two more than an even number in terms of an integer n?
- 26th February 2015y is inversely proportional to x^2. When x = 2, y = 16. Work out y when x = 4.
- 27th February 2015In a circle theorem proof, a step uses the fact that opposite angles of a cyclic quadrilateral are being proved. State the reason being quoted.
- 28th February 2015The probability of winning a game is 7/8. A player expects 63 wins. How many games did they play?