Daily Practice · Higher Plus
January 2015 - Higher Plus 5-a-day
Every Higher Plus sheet published in January 2015, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' January 2015 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in January 2015
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st January 2015Simplify sqrt(50) + sqrt(50), giving your answer in the form a sqrt(b).
- 2nd January 2015The point (1, -1) lies on y = f(x). Write down its image on y = f(x - 4).
- 3rd January 2015A train slows steadily from 31 m/s to rest in 8 seconds. Work out its deceleration.
- 4th January 2015In a vector proof you find that vector PQ = 2a + 6b and vector RS = 8a + 24b. What does this show about PQ and RS?
- 5th January 2015A bag holds 5 red and n blue counters. The probability of taking a red is 5/8. Work out n.
- 6th January 2015A histogram has two bars: one 5 units wide with frequency density 0.4, one 10 units wide with density 3. How many values in total?
- 7th January 2015A rectangle is 19 cm by 29 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 8th January 2015Prove that the sum of 7 consecutive integers is always a multiple of 7. State the simplified sum you would use.
- 9th January 2015y is inversely proportional to x^2. When x = 3, y = 144. Work out y when x = 6.
- 10th January 2015A cuboid measures 5 cm by 8 cm by 15 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 11th January 2015A bag holds 7 red and 3 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 12th January 2015On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 13th January 2015Expand and simplify (9 + sqrt(6))(9 - sqrt(6)).
- 14th January 2015f(x) = 3x - 1 and g(x) = 4x - 7. Work out fg(5).
- 15th January 2015y is directly proportional to x^3. When x = 4, y = 256. Work out y when x = 2.
- 16th January 2015A cuboid measures 10 cm by 5 cm by 4 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 17th January 2015A bag holds 6 red, 6 blue and 5 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 18th January 2015A histogram has two bars: one 5 units wide with frequency density 2.5, one 25 units wide with density 0.8. How many values in total?
- 19th January 2015A block has mass 700 g (to the nearest 10 g) and volume 19 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 20th January 2015The curve y = sin x° is drawn for 0 <= x <= 360. Write down the value of y when x = 360.
- 21st January 2015y is directly proportional to sqrt(x). When x = 36, y = 48. Work out y when x = 16.
- 22nd January 2015The point (20, 21) lies on the circle x^2 + y^2 = 841. Work out the gradient of the tangent to the circle at that point.
- 23rd January 2015A bag holds 12 counters, r of them red. Two are taken without replacement and P(both red) = 15/22. Work out r.
- 24th January 2015On a histogram, a 5-wide bar and a 20-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 25th January 2015x = 129 and y = 15, each correct to the nearest whole number. Work out the upper bound of x - y.
- 26th January 2015A quadratic sequence starts -3, 1, 7, 15. Work out the second difference, and the coefficient of n^2.
- 27th January 2015A train slows steadily from 32 m/s to rest in 5 seconds. Work out its deceleration.
- 28th January 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.
- 29th January 2015The probability of winning a game is 1/5. A player expects 10 wins. How many games did they play?
- 30th January 2015A histogram has two bars: one 10 units wide with frequency density 1.2, one 10 units wide with density 0.6. How many values in total?
- 31st January 2015A car covers 230 m (to the nearest 10 m) in 5 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.