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Year 10 Mathematics sample

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Question 1 of 5 Space and geometry

A window grille panel is a diamond shape with all four sides the same length. One straight bar runs across it from the left corner to the right corner. Where the bar meets the side at the left corner it makes an angle of 24 degrees. How big is the whole corner angle at the top of the panel, marked x?

Window grille24 degreesxAll four sides of the panel are cut to the same length.The bar and two sides of the panel make one triangle.
Question 2 of 5 Number and arithmetic

Every batch of rails leaving a bike frame builder is checked against a target length of 500 mm. A piece passes only when its length is no more than 1.2 per cent away from that target. The table lists the 6 pieces measured this morning. How many of them pass?

Lengths measured this morning
PieceLength measured
Rail P493 mm
Rail Q508 mm
Rail R495 mm
Rail S505 mm
Rail T500 mm
Rail U507 mm
Question 3 of 5 Measures and units

A strip of ground at a caravan park lies between two straight paths that run parallel to one another. The strip measures 38 m along one path and 32 m along the other. Mulch is spread over the whole strip at $6.40 for each square metre, and the bill comes to $2688.00. How far apart are the two paths?

Caravan park strip32 m along this pathhow far across?38 m along this pathThe plan is not drawn to scale.The two paths stay the same distance apart the whole way.
Question 4 of 5 Algebra and patterns

Before its fundraiser, a scout group printed a run of art union tickets. In the first week it sold \(\frac{1}{3}\) of the whole run. In the second week it sold another 45 tickets. When the draw closed, \(\frac{1}{6}\) of the whole run had never been sold. How many tickets were printed?

What happened to the print run
Second week sales: 45 tickets The two fractions are shares of the WHOLE run, not of what was left.
  1. Every printed ticket ended up in one of three groups and no ticket is counted twice.
  2. Sold in the first week: 33.3 per cent of the run.
  3. Sold in the second week: 45 tickets.
  4. Never sold: 16.7 per cent of the run.
  5. No extra tickets were printed once the fundraiser began.
Question 5 of 5 Chance and data

A ranger at a farm dam nets 60 yabbies, clips a small tag to each one and returns them all to the water. A week later the same net is worked over the same ground and brings up 35 yabbies, of which 7 carry a tag. Using the record, what is the best estimate of how many yabbies live there?

Dam tagging record
Stage of the countNumber of yabbies
Tagged and returned to the water60
Netted in the second haul35
Tagged animals inside that second haul7
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