Daily Practice · Higher Plus
March 2014 - Higher Plus 5-a-day
Every Higher Plus sheet published in March 2014, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' March 2014 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in March 2014
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st March 2014A car covers 780 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.
- 2nd March 2014The point (0, -6) lies on y = f(x). Write down its image on y = -f(x).
- 3rd March 2014y is inversely proportional to x^2. When x = 2, y = 48. Work out y when x = 4.
- 4th March 2014In a circle theorem proof, a step uses the fact that OA and OB are both radii of the circle, so triangle OAB is isosceles. State the reason being quoted.
- 5th March 2014The probability of winning a game is 1/4. A player expects 20 wins. How many games did they play?
- 6th March 2014On a histogram, a 5-wide bar and a 10-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 7th March 2014Rationalise the denominator of 22/sqrt(11), giving your answer in its simplest form.
- 8th March 2014Prove that the sum of 3 consecutive integers is always a multiple of 3. State the simplified sum you would use.
- 9th March 2014y is directly proportional to x^3. When x = 3, y = 135. Work out y when x = 4.
- 10th March 2014In a vector proof you find that vector PQ = 6a - 5b and vector RS = 18a - 15b. What does this show about PQ and RS?
- 11th March 2014A bag holds 2 red and n blue counters. The probability of taking a red is 2/7. Work out n.
- 12th March 2014A histogram has two bars: one 5 units wide with frequency density 2.5, one 20 units wide with density 1.4. How many values in total?
- 13th March 2014Simplify sqrt(50) + sqrt(72), giving your answer in the form a sqrt(b).
- 14th March 2014f(x) = 5x + 9 and g(x) = 5x + 6. Work out fg(0).
- 15th March 2014y is directly proportional to sqrt(x). When x = 25, y = 35. Work out y when x = 9.
- 16th March 2014A cuboid measures 15 cm by 6 cm by 3 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 17th March 2014A bag holds 7 red and 7 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 18th March 2014On a histogram, a 10-wide bar and a 30-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 19th March 2014A rectangle is 25 cm by 24 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 20th March 2014The curve y = sin x° is drawn for 0 <= x <= 360. Write down the value of y when x = 90.
- 21st March 2014A train slows steadily from 13 m/s to rest in 4 seconds. Work out its deceleration.
- 22nd March 2014A cuboid measures 14 cm by 7 cm by 10 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 23rd March 2014A bag holds 4 red, 5 blue and 4 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 24th March 2014A histogram has two bars: one 10 units wide with frequency density 0.4, one 20 units wide with density 3. How many values in total?
- 25th March 2014Expand and simplify (8 + sqrt(3))(8 - sqrt(3)).
- 26th March 2014A quadratic sequence starts 10, 19, 32, 49. Work out the second difference, and the coefficient of n^2.
- 27th March 2014y is inversely proportional to x^2. When x = 2, y = 72. Work out y when x = 6.
- 28th March 2014The point (6, 8) lies on the circle x^2 + y^2 = 100. Work out the gradient of the tangent to the circle at that point.
- 29th March 2014A bag holds 5 counters, r of them red. Two are taken without replacement and P(both red) = 1/10. Work out r.
- 30th March 2014On a histogram, a 10-wide bar and a 30-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 31st March 2014A block has mass 620 g (to the nearest 10 g) and volume 4 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.