Daily Practice · Higher Plus
March 2007 - Higher Plus 5-a-day
Every Higher Plus sheet published in March 2007, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' March 2007 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in March 2007
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st March 2007A histogram has two bars: one 5 units wide with frequency density 0.4, one 25 units wide with density 1.4. How many values in total?
- 2nd March 2007Rationalise the denominator of 12/sqrt(6), giving your answer in its simplest form.
- 3rd March 2007Work out the nth term of the quadratic sequence 12, 20, 32, 48, ...
- 4th March 2007y is directly proportional to sqrt(x). When x = 4, y = 18. Work out y when x = 49.
- 5th March 2007The 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.
- 6th March 2007A bag holds 12 counters, r of them red. Two are taken without replacement and P(both red) = 5/33. Work out r.
- 7th March 2007On a histogram, a 4-wide bar and a 12-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 8th March 2007Simplify sqrt(32) + sqrt(98), giving your answer in the form a sqrt(b).
- 9th March 2007The point (-1, 6) lies on y = f(x). Write down its image on y = f(-x).
- 10th March 2007A train slows steadily from 19 m/s to rest in 10 seconds. Work out its deceleration.
- 11th March 2007In a circle theorem proof, a step uses the fact that two angles at the circumference stand on the same arc. State the reason being quoted.
- 12th March 2007The probability of winning a game is 1/2. A player expects 6 wins. How many games did they play?
- 13th March 2007A histogram has two bars: one 10 units wide with frequency density 1.2, one 25 units wide with density 3.5. How many values in total?
- 14th March 2007A rectangle is 27 cm by 27 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 15th March 2007Prove that the sum of 9 consecutive integers is always a multiple of 9. State the simplified sum you would use.
- 16th March 2007y is inversely proportional to x^2. When x = 2, y = 36. Work out y when x = 6.
- 17th March 2007In a vector proof you find that vector PQ = 6a + 3b and vector RS = 18a + 9b. What does this show about PQ and RS?
- 18th March 2007A bag holds 7 red and n blue counters. The probability of taking a red is 7/13. Work out n.
- 19th March 2007On 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?
- 20th March 2007Expand and simplify (4 + sqrt(3))(4 - sqrt(3)).
- 21st March 2007f(x) = 2x + 5 and g(x) = 5x - 7. Work out fg(6).
- 22nd March 2007y is directly proportional to x^3. When x = 2, y = 32. Work out y when x = 4.
- 23rd March 2007A cuboid measures 9 cm by 6 cm by 8 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 24th March 2007A bag holds 3 red and 5 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 25th March 2007A histogram has two bars: one 5 units wide with frequency density 1.5, one 20 units wide with density 3. How many values in total?
- 26th March 2007A block has mass 520 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.
- 27th March 2007The curve y = cos x° is drawn for 0 <= x <= 360. Write down the value of y when x = 270.
- 28th March 2007y is directly proportional to sqrt(x). When x = 16, y = 36. Work out y when x = 36.
- 29th March 2007A cuboid measures 13 cm by 10 cm by 8 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 30th March 2007A bag holds 6 red, 3 blue and 5 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 31st March 2007On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 1.5. How many more values are in the wider class?